Question

How do you simplify square root of 70 / square root of 40?

Answer 1

`sqrt(70) / sqrt(40) = sqrt(7)/2`

Explanation:

Using prime factorization, `sqrt(70) / sqrt(40)` can be rewritten as `sqrt(7*5*2) / sqrt(5*2^3`

`sqrt(5*2)` is found in both the numerator and denominator and cancel each other out:

`sqrt(7*5*2) / sqrt(5*2^3) = sqrt(7) / sqrt( 2^2)`

The denominator `sqrt( 2^2)`, or `sqrt(4)`, is a perfect square which simplifies to `2`:

`sqrt(7) / sqrt( 2^2) = sqrt(7)/2`

This is the simplified expression.