Question

How do you calculate the square root of $ 20 $ divided by the square root of $ 15 $ ?

Answer 1

Hint: As we know that square root can be defined as a number which when multiplied by itself gives a number as the product. For example $ 5\times 5 = 25 $ , here square root of $ 25 $ is $ 5 $ . There is no such formula to calculate square root formula but two ways are generally considered. They are the prime factorization method and division method.

Complete step-by-step answer:
First we should rewrite the equation in mathematical term:
 $ \dfrac{{\sqrt {20} }}{{\sqrt {15} }} $ .
Now we should write each numerator and denominator in their multiples form, so
 $ \sqrt {20} $ can be written as $ \sqrt 5\times\sqrt 4 $ and $ \sqrt {15} $ can be written multiples of $ \sqrt 5\times\sqrt 3 $ , by putting the values in fraction we get,
 $ \dfrac{{\sqrt 5 \sqrt 4 }}{{\sqrt 5 \sqrt 3 }} $ $ = \dfrac{{\sqrt 5\times 2}}{{\sqrt 5 \sqrt 3 }} $ , as $ 4 $ is the square root of $ 2 $ .
Now we have a common factor of $ \sqrt 5 $ in both the numerator and the denominator, so we can eliminate it. It gives us a simplified value i.e.
$ \dfrac{2}{{\sqrt 3 }} $ .
Hence the required answer is $ \dfrac{2}{{\sqrt 3 }} $ .
So, the correct answer is “ $ \dfrac{2}{{\sqrt 3 }} $ ”.

Note: The above given numbers are non-perfect squares as we know that a non-perfect square is a number that there is no rational number i.e. it is considered as an irrational number. Their decimal does not end and they do not repeat a pattern so they are also non-terminating and non-repeating numbers. We know that all real numbers have two square roots, one is a positive square root and another one is a negative square root. The positive square root is also referred to as the principal square root.