Question

How do you simplify `sqrt15/(2sqrt20)`?

Answer 1

Take squares out of square roots.

Explanation:

Original expression: `sqrt(15)/(2sqrt(20))`

Using prime factorization for the values inside the square roots:
`=sqrt(3*5)/(2sqrt(2^2*5)`

Take out the `2^2` out of the square root in the denominator:
`=sqrt(3*5)/(4sqrt(5))`

Combine the square roots into one square root:
`=1/4sqrt((3*5)/5)`

Cancel the `5` in the numerator and denominator of the square root:
`=sqrt(3)/4` which is our final answer.