Question

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

Answer 1

Eliminate common factors and you will find the answer is $\frac{2}{\sqrt{3}}$
Explanation:
First, let's write the expression:
$\frac{\sqrt{20}}{\sqrt{15}}$
Now, we factor each number down:
$\frac{\sqrt{20}}{\sqrt{15}}=\frac{\sqrt{5}\sqrt{4}}{\sqrt{5}\sqrt{3}}$
$=\frac{2\sqrt{5}}{\sqrt{5}\sqrt{3}}$
We have a common factor of $\sqrt{5}$ in both numerator and denominator, and can therefore eliminate:
$=\frac{2\sqrt{5}}{\sqrt{5}\sqrt{3}}$
We now have our simplified answer.
$\frac{2}{\sqrt{3}}$