How to of the Day

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• How to Decide Between the Peloton Bike and Bike Plus
• How to Make Your Own Beauty Products
• How to Simplify Radical Expressions

How to Decide Between the Peloton Bike and Bike Plus Posted: 12 Sep 2021 05:00 PM PDT If you're considering buying from Peloton, you've already landed on one of the best brands for at-home fitness. Once you have settled on a Peloton subscription, all you need is your own equipment! Peloton's bikes are top of the class, but with new releases and classic bikes, which one is right for you? There are a few important aspects you'll want to consider: size, price, and versatility, to name a few. Read on for an in-depth review of the Peloton Bike and the Peloton Bike+. [Edit]Steps [Edit]The Peloton Bike The original Peloton bike has a smaller frame and a smaller sticker price than its successor, but fewer add-ons. The Peloton bike boasts the ability to partake in the Peloton series spin classes with its touch screen and magnetic resistance knob. Price. The Peloton Bike is Peloton's cheapest bike ever. As of September 2021, the Peloton Bike starts at $1,495, or a monthly payment of $39. Size. This bike has a 4' by 2' footprint, making it easy to store in any corner of your home. The bike also comes with a 21.5'' HD touch screen, though it does not rotate like the Bike+. The screen may make it a little harder to do off-bike classes (like strength training), but not impossible. Features. With a Peloton All-Access subscription ($39/month), you receive access to live classes, individual profiles for household members, live mid-workout fitness metrics, leaderboards to compete against other Peloton members, and special event programming. [1] Final thoughts. The Peloton Bike is best for people purchasing their first at-home cycling bike or people who don't want to spend too much on an at-home workout system. [Edit]The Peloton Bike+ The Peloton Bike + is the newest high-end Peloton, adding features to the original for cyclers seeking more variety and control in their at-home workouts. Though this Peloton offering is the most expensive bike, you pay for a large rotating screen, high-quality cardio equipment, and a great sound system.[2] Price. This model is a bit pricier than the original, starting at $2,495 with a $64-month membership fee for classes and workouts. Size. The Bike+ has the same 4' by 2' footprint as the original Peloton Bike, but it is six inches taller. The 23.8" HD touch screen rotates 180 degrees for classes where you may need to get off your bike so the Bike+ will require a little more space. The Bike+ also weighs 140 pounds, five pounds more than the Bike. Features. With a Peloton All-Access subscription ($39/month), you receive access to live classes, individual profiles for household members, live mid-workout fitness metrics, leaderboards to compete against other Peloton members, and special event programming. Apple Gym Kit Integration. With this feature, you can pair your Apple Watch with the Bike+ to sync your performance metrics between the two devices including heart rate, energy output, and more. This makes keeping track of your fitness metrics easier and more efficient than ever. Resistance Knob Auto Follow. Although the Peloton Bike comes with a resistance knob, some classes will ask you to adjust your resistance during class to make cycling easier or harder. The Peloton Bike+ will automatically adjust to the instructor's recommended resistance, so you can stay on track without having to pause your workout. Final thoughts. The Peloton Bike+ is best for serious at-home bikers who are ok with spending more to access the special features that come with it. [Edit]Other Major Differences Between The Bikes Besides price and the additional features like Auto Follow and Apple GymKit on the Bike+, there are a few other notable differences between the two bikes. Sound System. The Bike+ has 4-channel audio with 2x3 watt tweeters and 2x10 watt woofers, while the Bike has a 2x10 watt sound system. [3] If those technical terms don't mean much to you, know that the Bike+ has a more intense, richer sound system than the Bike. Both bikes are compatible with Bluetooth. Tech. The Bike+ comes with a USB-C charging port while the Bike comes with a USB port. If you want to charge your other devices while riding, you might consider which ports best serve you. [4] It's a win-win. In our opinion, you can't go wrong with either of these Peloton models, but hopefully these quick metrics have given you a better idea on which one will be your ideal bike. Happy cycling! [Edit]References ↑ https://www.onepeloton.com/bikes/compare ↑ https://www.insider.com/peloton-review#peloton-bike-1 ↑ https://www.onepeloton.com/bikes/compare ↑ https://www.cnet.com/health/fitness/peloton-bike-vs-peloton-bike-plus-which-should-you-buy/

How to Make Your Own Beauty Products Posted: 12 Sep 2021 09:00 AM PDT Are you interested in making makeup, hair, and skincare products for yourself or to start your own line of beauty products? You don't need to have fancy or expensive ingredients to make beauty products on your own. In fact, you probably have most of the necessary ingredients in your home already! Making your own beauty products at home is as simple as gathering the materials and mixing them together. Doing so will save you money and keep you looking your best! [Edit]Steps [Edit]Creating Skincare Products Create a body wash using honey, coconut oil, and castile soap. Use of each ingredient. Stir them together in a glass or plastic container. Then, apply to a wet washcloth, pouf, or straight onto your body in the shower. Lather up, then rinse away the soap.[1] If desired, you may also add a 10 to 15 drops of an essential oil to give your body wash a nice scent, such as lavender, peppermint, chamomile, or orange. Make a body scrub with equal parts sugar and oil. Combine 1/2 cup (120 g) of sugar and 1/2 cup (120 mL) of olive or coconut oil in a glass or plastic container. Stir to combine the ingredients together. Apply the scrub to your skin in the shower and work it around to slough off dry, dead skin. Rinse thoroughly to remove the remaining scrub.[2] Add 1/2 tsp (2.5 mL) of vanilla extract to give your body scrub a pleasant scent.[3] Mix up some body oil using olive oil. Making your own lotion is a great way to ensure that only natural ingredients go into it, but if you don't have the time or ingredients, just use olive as lotion![4] Try adding a few drops of peppermint, lavender, lemon, or clary sage essential oil to give the oil a nice scent. Whip up a facial mask using ingredients in your kitchen. Facial masks come in many different varieties. You can make a facial mask using food from your kitchen and achieve the same results as a pre-made mask you'd find in a beauty supply store.[5] Combine 1/2 of an avocado, 1 tbsp (15 mL) of yogurt, and 1 tbsp (15 mL) of honey for a moisturizing mask. Whisk egg whites with orange juice and turmeric for a pore minimizing mask. Mix honey with cinnamon and lemon for a calming face mask. Stir raw oats into honey and mashed banana for a redness-reducing mask. [Edit]Making Haircare Products Create a simple shampoo using equal parts castile soap and water. Pour of castile soap and of water into a plastic or glass container. Then, stir the soap and water together gently to combine them. Wet your hair and apply a quarter-sized amount (about 15 mL) to your hair. Work it in with your fingertips and then rinse it away.[6] Mix in 1 tbsp (15 mL) of olive oil for a moisturizing shampoo. Add 2 to 3 drops of essential oil to create a scented shampoo. Mix up your own conditioner using ingredients from your kitchen. Mix 1 mashed banana or avocado, or of plain, whole-milk yogurt with 1 tsp (5 mL) of coconut or olive oil, and 1 tsp (5 mL) of honey. Apply the conditioner to your hair after you shampoo it. Let it sit for about 3 minutes, then rinse your hair thoroughly to get all of the conditioner out.[7] Keep in mind that this mixture won't keep at room temperature. Put it in an air-tight container and store it in the fridge for up to 1 week. If you want something you can spritz into your hair to help detangle it, make a leave-in conditioner. Combine gelatin and water for a natural hairspray. Add 1 tsp (5 g) of gelatin to of hot water. Stir the gelatin into the water until it dissolves. Let the water cool, and then transfer the gelatin hairspray to a spray bottle. Spritz it onto wet or dry hair as needed.[8] You can store the hairspray at room temperature for about 6 months, but shake it before each use as the gelatin may separate from the water. Make hair gel out of aloe vera gel. Purchase pure aloe vera gel from a store, measure out 1/2 cup (120 mL). Mix in about 20 drops of essential oil if desired to add scent to the hair gel.[9] Store the hair gel in an air-tight container and keep it at room temperature for up to 3 months. [Edit]Mixing up Your Own Makeup Combine beeswax, coconut oil, and cocoa butter for lip balm. Combine 1/4 cup (60 g) of grated beeswax, 2 tbsp (30 mL) of cocoa butter, 3 tbsp (45 mL) of coconut oil, and 1 tbsp (15 mL) of almond oil in a glass or plastic container. Melt the ingredients by microwaving them for 15 seconds at a time and stirring.[10] Transfer the lip balm to small containers or lip balm pots while it is still warm and let it cool. The lip balm will become solid when it is cool. Apply to your lips as needed. Make eye shadow using eye shadow pigments. You can purchase eye shadow pigments online and combine different colors to create your own custom eye shadow. Keep the powder loose, or mix about 1 tsp (5 g) of pigment with a few drops of isopropyl alcohol to form a paste that you can transfer to an eye shadow pan. Press the paste with a paper towel to remove the excess liquid.[11] Make sure that the pigments you use to make eyeshadow are safe to use for eye makeup! Create your own mascara. Making your own mascara is easy with a few special ingredients! Combine 2 tsp (10 mL) of coconut oil, 4 tsp (20 mL) of pure aloe vera, and 1 tsp (5 g) of grated beeswax in a small pan. Melt the ingredients over low heat on your stove, then remove them from the heat. Then, add about 1/2 tsp (2.5 g) of activated charcoal or cocoa powder to the mixture and stir to combine them. Transfer the liquid to a clean mascara tube.[12] Charcoal will make your mascara black, while cocoa powder will make it brown. [Edit]Warnings Always read the instructions for use of essential oils very carefully as some may react with others and most should be used in very specific quantities only. Test for allergic reactions first (or ask the pharmacist for more information) and if pregnant, only use oils with a physician's agreement. Never use any of the above products if they contain an ingredient you are allergic to. If you are allergic to bee pollen, you may be allergic to honey. Do not use any of the above containing honey if you are at risk for allergic reaction. If any irritation occurs, discontinue use immediately. Individual skin sensitivity can include skin irritation, breathing problems, sneezing and rashes. If you choose to wash your hair with egg, be sure not to use water that is too hot, or you'll end up with scrambled eggs in your hair, literally! [Edit]Related wikiHows Admit to a Foot Fetish Make a Sugar and Coffee Scrub [Edit]References ↑ https://www.youtube.com/watch?v=W-Ir-nARC-A&feature=youtu.be&t=36 ↑ https://keeperofthehome.org/how-to-make-your-own-natural-skin-care-products-diyfriday/ ↑ https://www.treehugger.com/organic-beauty/8-homemade-salt-and-sugar-body-scrubs.html ↑ https://keeperofthehome.org/how-to-make-your-own-natural-skin-care-products-diyfriday/ ↑ https://www.self.com/gallery/7-easy-diy-face-masks ↑ https://www.goodhousekeeping.com/beauty/hair/a20705785/homemade-shampoo-conditioner-recipes/ ↑ https://www.today.com/style/make-your-own-all-natural-shampoo-under-buck-more-diys-t74161 ↑ https://keeperofthehome.org/how-to-make-your-own-natural-skin-care-products-diyfriday/ ↑ https://www.mommypotamus.com/diy-hair-gel/ ↑ https://keeperofthehome.org/how-to-make-your-own-natural-skin-care-products-diyfriday/ ↑ https://www.youtube.com/watch?v=Ep0_gGBgsdk&feature=youtu.be&t=24 ↑ https://www.thankyourbody.com/all-natural-homemade-mascara/

How to Simplify Radical Expressions Posted: 12 Sep 2021 01:00 AM PDT Radicals, also called roots, are the opposite of exponents. They even sound like opposites when we're talking about them out loud: we say ${\displaystyle 6^{2}}$ is "six squared", and ${\displaystyle {\sqrt {6}}}$ is "the square root of six". And just like we can use larger and larger exponents like ${\displaystyle ^{3}}$ and ${\displaystyle ^{4}}$, we can also find smaller and smaller roots like ${\displaystyle {\sqrt[{3}]{}}}$ and ${\displaystyle {\sqrt[{4}]{}}}$. Simplifying radical expressions uses many of the same tricks you've learned in earlier math lessons for simplifying fractions or exponents. If you're new to the topic, start by learning how to simplify the square root of an integer. [Edit]Steps [Edit]Simplifying the Square Root of an Integer Factor the number under the square root. Ignore the square root for now and just look at the number underneath it. Factor that number by writing it as the product of two smaller numbers. (If the factors aren't obvious, just see if it divides evenly by 2. If not, try again with 3, then 4, and so on, until you find a factor that works.)[1] Example: Simplify ${\displaystyle {\sqrt {45}}}$. The first step is finding some factors of 45. You can't divide 45 by 2, so try dividing it by 3 instead: ${\displaystyle 45\div 3=15}$, so ${\displaystyle 45=3\times 15}$. ${\displaystyle {\sqrt {45}}={\sqrt {3\times 15}}}$ Keep going until the number is factored completely. Remember, any number can be factored down into prime numbers (like 2, 3, 5, and 7). Keep breaking down the factors until there are no more factors to find.[2] Now we have ${\displaystyle {\sqrt {3\times 15}}}$, but we can factor 15 again into ${\displaystyle 3\times 5}$. ${\displaystyle {\sqrt {45}}={\sqrt {3\times 3\times 5}}}$ Rewrite pairs of the same number as powers of 2. If the same factor shows up more than once, rewrite it as an exponent. (Keep everything underneath the square root.)[3] In ${\displaystyle {\sqrt {3\times 3\times 5}}}$, the number 3 shows up twice. Since ${\displaystyle 3\times 3=3^{2}}$, we can rewrite the whole expression as ${\displaystyle {\sqrt {3^{2}\times 5}}}$. Take any numbers raised to the power of 2 outside the square root. Roots and exponents are opposite, so they cancel each other out. If any factors are raised to the power of 2, move that factor in front of the square root (and get rid of the exponent).[4] ${\displaystyle {\sqrt {3^{2}\times 5}}={\sqrt {3^{2}}}{\sqrt {5}}}$ (As long as everything underneath the root is one multiplication problem, you can always rewrite the expression like this, with a root over each product.) ${\displaystyle {\sqrt {3^{2}}}{\sqrt {5}}=3{\sqrt {5}}}$ Since there are no other exponents left under the square root, you're all done! Simplify the result so there is no multiplication left. In more difficult problems, you might end up with multiple numbers in front of the square root, or underneath it. Solve these multiplication problems to simplify the answer. Example: Simplify ${\displaystyle {\sqrt {360}}}$. This takes a lot of factoring to break down: ${\displaystyle {\sqrt {360}}={\sqrt {40\times 9}}={\sqrt {(5\times 8)\times (3\times 3)}}={\sqrt {5\times 2\times 2\times 2\times 3\times 3}}}$ Rewrite pairs of numbers using exponents: ${\displaystyle {\sqrt {5\times 2^{2}\times 2\times 3^{2}}}}$. Bring the 2 and 3 outside the square root: ${\displaystyle 2\times 3\times {\sqrt {5\times 2}}}$ Simplify the numbers in front of the square root: ${\displaystyle 6{\sqrt {5\times 2}}}$ To get the final answer, simplify the numbers under the square root: ${\displaystyle 6{\sqrt {10}}}$ [Edit]Simplifying Cube Roots and Higher Roots Find the prime factors of the number under the root. Just like square roots, the first step to simplifying a cube root (${\displaystyle {\sqrt[{3}]{}}}$), a fourth root (${\displaystyle {\sqrt[{4}]{}}}$), or any higher root is to factor the number under the root.[5] Example: Simplify ${\displaystyle {\sqrt[{3}]{81}}}$ (the cube root of 81). ${\displaystyle 81=3\times 3\times 3\times 3}$, so ${\displaystyle {\sqrt[{3}]{81}}={\sqrt[{3}]{3\times 3\times 3\times 3}}}$ Rewrite groups of the same factors in exponent form. If the same prime factor shows up more than once, rewrite them as an exponent.[6] ${\displaystyle {\sqrt[{3}]{3\times 3\times 3\times 3}}={\sqrt[{3}]{3^{4}}}}$ Simplify the root of exponents wherever possible. Just as a square root cancels out a square, higher roots cancel out matching exponents (for instance, ${\displaystyle {\sqrt[{3}]{}}}$ and ${\displaystyle ^{3}}$). Check out this example to see how this works:[7] ${\displaystyle {\sqrt[{3}]{3^{4}}}={\sqrt[{3}]{3^{3}\times 3}}={\sqrt[{3}]{3^{3}}}{\sqrt[{3}]{3}}}$ Since the root and exponent match in ${\displaystyle {\sqrt[{3}]{3^{3}}}}$, they cancel out, leaving only the base number, ${\displaystyle 3}$. Plug that into the whole expression to get ${\displaystyle 3{\sqrt[{3}]{3}}}$. Since there are no more exponents left that can cancel out, this is the simplified form. Simplify any multiplication and exponents. You'll often end up with exponents that don't cancel out, or with more than one number multiplied together. Solve for these so you end up with one number outside the radical, and one number inside it. Example: Simplify ${\displaystyle {\sqrt[{5}]{2^{7}\times 3^{5}\times 7}}}$. This is already factored into prime numbers, so we can skip that step. Let's rewrite this as ${\displaystyle {\sqrt[{5}]{2^{7}}}{\sqrt[{5}]{3^{5}}}{\sqrt[{5}]{7}}}$. ${\displaystyle {\sqrt[{5}]{2^{7}}}={\sqrt[{5}]{2^{5}\times 2^{2}}}}$, by the rules of exponents. The root and exponent cancel out in the first term, leaving ${\displaystyle 2{\sqrt[{5}]{2^{2}}}}$ In ${\displaystyle {\sqrt[{5}]{3^{5}}}}$, the root and exponent cancel out to make ${\displaystyle 3}$. Since ${\displaystyle {\sqrt[{5}]{7}}}$ has no exponents that cancel out, this can't be simplified. Plug your simplified terms back into the whole expression: ${\displaystyle 2{\sqrt[{5}]{2^{2}}}\times 3\times {\sqrt[{5}]{7}}}$ Combine like terms: ${\displaystyle (2\times 3){\sqrt[{5}]{2^{2}\times 7}}}$ Calculate multiplication and exponents: ${\displaystyle 6{\sqrt[{5}]{28}}}$ [Edit]Simplifying Fractions inside Roots Simplify the fraction. What if a whole fraction is underneath a root? One way to solve problems like this is to ignore the radical expression at first. Simplify the fraction as much as you can, then see if the root lets you simplify further.[8] Example: Simplify ${\displaystyle {\sqrt {\frac {100}{4}}}}$. ${\displaystyle {\frac {100}{4}}=25}$, so we can rewrite this as ${\displaystyle {\sqrt {25}}}$. ${\displaystyle 25=5^{2}}$, so ${\displaystyle {\sqrt {25}}=5}$. Rewrite the fraction as two radical expressions instead. Some people prefer this other method of solving problems like this. Rewrite the fraction so there is one root in the numerator and another in the denominator. Simplify each root separately, then simplify the fraction.[9] Example: Simplify ${\displaystyle {\sqrt {\frac {75}{12}}}}$. Rewrite this as ${\displaystyle {\frac {\sqrt {75}}{\sqrt {12}}}}$. Simplify the numerator: ${\displaystyle {\sqrt {75}}={\sqrt {25\times 3}}=5{\sqrt {3}}}$ Simplify the denominator: ${\displaystyle {\sqrt {12}}={\sqrt {4\times 3}}=2{\sqrt {3}}}$ Plug these back into the fraction: ${\displaystyle {\frac {5{\sqrt {3}}}{2{\sqrt {3}}}}}$ Cancel out ${\displaystyle {\sqrt {3}}}$ to get ${\displaystyle {\frac {5}{2}}}$. Adjust your answer so there are no roots in the denominator. Sometimes, the simplest form still has a radical expression. That's fine, but most math teachers want you to keep any radicals in the top of the fraction, not the denominator. Follow the rules for multiplying fractions to cancel out any roots on the bottom of your fraction:[10] Example: You've simplified a fraction and got the answer ${\displaystyle {\frac {4}{9{\sqrt {5}}}}}$. To put it in standard form, multiply the top and bottom of the fraction by the root: ${\displaystyle {\frac {4\times {\sqrt {5}}}{9{\sqrt {5}}\times {\sqrt {5}}}}={\frac {4{\sqrt {5}}}{9\times 5}}={\frac {4{\sqrt {5}}}{45}}}$ [Edit]Combining Roots of Different Kinds Convert roots to fractional exponents. You can rewrite any root as an exponent with a fractional value. The pattern is pretty straightforward once you're used to it:[11] ${\displaystyle {\sqrt {x}}=x^{\frac {1}{2}}}$ ${\displaystyle {\sqrt[{3}]{x}}=x^{\frac {1}{3}}}$ ${\displaystyle {\sqrt[{4}]{x}}=x^{\frac {1}{4}}}$ ...and so on. Combine the terms using exponent rules. Once you've converted your terms to exponent form, follow the rules of exponents to combine them into a single expression.[12] Example: Write ${\displaystyle {\sqrt {3}}{\sqrt[{4}]{3}}}$ as one radical expression. Rewrite each term in exponent form: ${\displaystyle {\sqrt {3}}}$ becomes ${\displaystyle 3^{\frac {1}{2}}}$, and ${\displaystyle {\sqrt[{4}]{3}}}$ becomes ${\displaystyle 3^{\frac {1}{4}}}$. The whole expression is now ${\displaystyle 3^{\frac {1}{2}}\times 3^{\frac {1}{4}}}$. Since the exponents have the same base (3), multiplying them together gives us the same base raised to the sum of the two exponents: ${\displaystyle 3^{({\frac {1}{2}}+{\frac {1}{4}})}}$. Simplify to ${\displaystyle 3^{\frac {3}{4}}}$. Convert back to radical form. Once you have a single term with a fractional exponent, rewrite it as a radical expression. (The denominator moves to the root, and the numerator stays as an exponent.)[13] ${\displaystyle 3^{\frac {3}{4}}={\sqrt[{4}]{3^{3}}}}$ Simplify if possible. If you have any multiplication or exponents left, calculate them so your final answer is in simplest form. ${\displaystyle {\sqrt[{4}]{3^{3}}}={\sqrt[{4}]{9}}}$ [Edit]Simplifying Radical Expressions with Variables Cancel out exponents and roots just as you would with integers. Algebraic problems involve variables like ${\displaystyle x}$ that can represent any number. The rules for exponents and roots still apply to these variables.[14] Example: Simplify ${\displaystyle {\sqrt[{3}]{x^{2}\times x}}}$. Combine the terms under the cube root just like you would a number: ${\displaystyle {\sqrt[{3}]{x^{3}}}}$ Since the root and the exponent values match, they cancel out to make ${\displaystyle x}$. Give positive solutions to even roots. Notice how ${\displaystyle (-2)^{2}}$ and ${\displaystyle 2^{2}}$ both equal 4. That means that 4 (or any positive number) actually has two square roots: one positive number and one negative. But the square root symbol ${\displaystyle {\sqrt {}}}$, by default, only refers to the positive number. For instance, you can simplify ${\displaystyle {\sqrt {4}}}$ to ${\displaystyle 2}$, and ignore the negative solution.[15] The same is true of any even root: ${\displaystyle {\sqrt {}},{\sqrt[{4}]{}},{\sqrt[{6}]{}}}$, and so on. This does not apply to odd roots like ${\displaystyle {\sqrt[{3}]{}}}$ or ${\displaystyle {\sqrt[{5}]{}}}$. The odd root of a negative number is always negative, and the odd root of a positive number is always positive. (Test this yourself by calculating ${\displaystyle 2^{3}}$ and ${\displaystyle (-2)^{3}}$.) Use the absolute value symbol to make a variable positive. Variables are tricky: we don't know whether they represent a positive or a negative number. Since the square root (or any even root) function must always give a positive answer, we make sure this happens by using the absolute value symbol around the answers, like this: |x|. This symbol just means "make this value positive."[16] Example: Simplify ${\displaystyle {\sqrt {32x^{2}}}}$. Simplify the non-variable term: ${\displaystyle {\sqrt {32}}={\sqrt {2^{2}\times 2^{2}\times 2}}=(2\times 2){\sqrt {2}}=4{\sqrt {2}}}$. Simplify the variable component by canceling out the root and exponent: ${\displaystyle {\sqrt {x^{2}}}=x}$. To make sure the solution to the root is positive, add absolute value symbols around that term: |x|. Write the whole expression: 4|x|${\displaystyle {\sqrt {2}}}$. [Edit]Video [Edit]Tips You can find online tools or apps that will simplify a radical expression for you. You can use these to check your work. For complicated problems, you might need to use more than one of these methods. (For instance, you might first multiply a square root with a cube root, then simplify further, then simplify a fraction.) Make "easy" simplifications as you go (for instance, 4/2=2 or 3x5=15) and you'll have an easier time. [Edit]Warnings The square root (or any even root) of a negative number can't be simplified without using complex numbers. For now, leave expressions like ${\displaystyle {\sqrt {-4}}}$ alone, and treat them as separate from the rest of the expression. (Odd roots like ${\displaystyle {\sqrt[{3}]{}}}$ or ${\displaystyle {\sqrt[{5}]{}}}$ can handle negative numbers just fine.)[17] [Edit]Related wikiHows Solve Radical Equations [Edit]References [Edit]Quick Summary ↑ https://www.mesacc.edu/~scotz47781/mat120/notes/radicals/simplify/simplifying.html ↑ https://www.purplemath.com/modules/factnumb.htm ↑ https://www.khanacademy.org/math/algebra-2018/rational-exponents-and-radicals/alg1-simplify-square-roots/a/simplifying-square-roots-review ↑ https://www.khanacademy.org/math/algebra-2018/rational-exponents-and-radicals/alg1-simplify-square-roots/a/simplifying-square-roots-review ↑ https://www.mesacc.edu/~scotz47781/mat120/notes/radicals/simplify/simplifying.html ↑ https://mathbitsnotebook.com/Algebra2/Radicals/RDSimplifyingRadicalsCubeRoots.html ↑ https://mathbitsnotebook.com/Algebra2/Radicals/RDSimplifyingRadicalsCubeRoots.html ↑ https://www.purplemath.com/modules/radicals4.htm ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm ↑ https://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U16_L1_T3_text_final.html ↑ https://www.purplemath.com/modules/radicals7.htm ↑ https://www.purplemath.com/modules/radicals7.htm ↑ https://mathbitsnotebook.com/Algebra2/Radicals/RDSimplifyingRadicalsCubeRoots.html ↑ https://www.learnalberta.ca/content/memg/Division03/Principal%20Square%20Root/ ↑ http://matcmath.org/press/6-1-simplifying-expressions-with-roots-and-fractional-exponents/ ↑ http://matcmath.org/press/6-1-simplifying-expressions-with-roots-and-fractional-exponents/

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