Question

What is the square root of $\dfrac{20}{125}$?

Answer 1

Hint: First we will simplify the given fraction. We will write the given numbers 20 and 125 into simplest factors. Then cancelling out the common factors we will get the desired answer.

Complete step by step solution:
We have been given a fraction $\dfrac{20}{125}$.
We have to find the square root of a given fraction.
Now, let us first simplify the given fraction. For this we will write the factors of 20 and 125. Then we will get
$\Rightarrow \dfrac{2\times 2\times 5}{5\times 5\times 5}$
Now, cancelling out the common terms we will get
$\Rightarrow \dfrac{2\times 2}{5\times 5}$
Now, we have to find the square root of the above obtained expression. Then we will get
$\Rightarrow \sqrt{\dfrac{2\times 2}{5\times 5}}$
Now, we know that to find the square root we have to make a pair of two numbers. In the above equation both the numbers are perfect squares. So we can take one outside the square root.
Now, simplifying the above obtained equation we will get
$\Rightarrow \dfrac{2}{5}$
Hence above is the required square root of the given fraction.

Note: As the given numbers 20 and 125 both are not perfect squares. So we need to simplify the given fractions because we cannot find the square roots of imperfect squares directly. If we have numbers such as 4, 25, 36 which are perfect squares then we can directly write the square roots of such numbers.