Question

How do you simplify $\sqrt{\dfrac{400}{5}}$ ?

Answer 1

Hint: We know the formula in exponential function $\sqrt{\dfrac{a}{b}}$ is equal to $\dfrac{\sqrt{a}}{\sqrt{b}}$ where b is not equal to 0 , first we can find the square root of a and divide it by square root by b. We can use this to simplify $\sqrt{\dfrac{400}{5}}$. First we will evaluate the square root of 400 and then divide it with the square root of 5.

Complete step-by-step answer:
We have to evaluate the value of $\sqrt{\dfrac{400}{5}}$ , we know that $\sqrt{\dfrac{a}{b}}$ is equal to $\dfrac{\sqrt{a}}{\sqrt{b}}$
So $\sqrt{\dfrac{400}{5}}$ is equal to $\dfrac{\sqrt{400}}{\sqrt{5}}$
We know that the square of 20 is equal to 400, so the square root of 400 is equal to 20.
So we can write $\dfrac{\sqrt{400}}{\sqrt{5}}$ = $\dfrac{20}{\sqrt{5}}$
We can further solve , we can multiply $\sqrt{5}$ to both numerator and denominator of $\dfrac{20}{\sqrt{5}}$ to make the denominator rational
So we can write $\dfrac{20}{\sqrt{5}}$ = $\dfrac{20\sqrt{5}}{5}$
Now we can cancel out 5
$\Rightarrow \dfrac{20\sqrt{5}}{5}=4\sqrt{5}$

Note: We can solve it by another method we can first divide 400 by 5 and then take the square root of it. So $\sqrt{\dfrac{400}{5}}$ is equal to the square root of 80 . To simplify the square root of 80 we can write 80 as its product of all prime factors. So 80 = $2\times 2\times 2\times 2\times 5$ square root of 80 is equal to $\sqrt{2\times 2\times 2\times 2\times 5}$ which is equal to $4\sqrt{5}$ . When we write the formula $\sqrt{\dfrac{a}{b}}$ is equal to $\dfrac{\sqrt{a}}{\sqrt{b}}$ we should always mention that the value of b should not be equal to 0, because we can not make denominator 0.