Square Root Of 20 color blue 2sqrt5 Here we prime factorise 20 in order to simplify the expression sqrt 20 sqrt 2 2 5 sqrt 2 2 5 color blue 2sqrt5
Simplifying sqrt20 by prime factorisation sqrt20 sqrt 2 2 5 color blue 2sqrt5 The expression can now be written as You need to multiply sqrt 10 and sqrt 20 Before doing that take a look at sqrt 20 Notice that you can write it as sqrt 20 sqrt 2 10 If you use the product property of radicals which tells you that color blue sqrt a b sqrt a sqrt b you can write sqrt 2 10 sqrt 2 sqrt 10 Your expression will now be
Square Root Of 20
Square Root Of 20
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There are two common ways to simplify radical expressions depending on the denominator Using the identities sqrt a 2 a and a b a b a 2 b 2 in fact you can get rid of the roots at the denominator 8sqrt5 using the color blue law of radicals color white x sqrtaxxsqrtb sqrt ab rArr4sqrt20 4xxsqrt 4xx5 4xxsqrt4xxsqrt5 4xx2xxsqrt5 8sqrt5
We first simplify sqrt20 and sqrt45 terms by prime factorisation sqrt20 sqrt 2 2 5 color bluw 2sqrt5 sqrt 20 sqrt 2 2 5 Taking the squared terms outside the radical taking the square roots whilst doing this and presuming that the use of the radical sign implies that only the positive square root is intended sqrt 80 4 sqrt 5 and sqrt 20 2 sqrt 5 Both terms now comprise the same radical sqrt 5 but with different
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The rule for multiplying square roots is that sqrta sqrtb sqrt ab It s important to clarify that because it can be confusing if you don t understand that radical multiplication is just like normal multiplication Anyway all we have to do now is apply this property sqrt20 sqrt5 sqrt 20 5 sqrt100 10 Final Answer If you are looking for an analytical solution sqrt 20 2 sqrt 4 5 2 cancel2sqrt5 cancel2 sqrt 5
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color blue 2sqrt5 Here we prime factorise 20 in order to simplify the expression sqrt 20 sqrt 2 2 5 sqrt 2 2 5 color blue 2sqrt5
https://socratic.org/questions/what-is-the-square-root-of-5-plus-the-squa…
Simplifying sqrt20 by prime factorisation sqrt20 sqrt 2 2 5 color blue 2sqrt5 The expression can now be written as
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Square Root Of 20 - sqrt 20 sqrt 2 2 5 Taking the squared terms outside the radical taking the square roots whilst doing this and presuming that the use of the radical sign implies that only the positive square root is intended sqrt 80 4 sqrt 5 and sqrt 20 2 sqrt 5 Both terms now comprise the same radical sqrt 5 but with different
