Question

How do you simplify `sqrt(15/36)`?

Answer 1

`sqrt(15/36) = sqrt(15)/6`

Explanation:

Here are a couple of identities we will use:

If `a >= 0` and `b > 0` then:

`sqrt(a/b) = sqrt(a)/sqrt(b)`

If `a >= 0` then:

`sqrt(a^2) = a`

`color(white)()`
Example

When given `sqrt(15/36)` to simplify, you could simplify `15/36` first, split the square root, then rationalise the denominator, but that would be missing out on the fact that `36=6^2` is already a perfect square.

Instead, we can proceed as follows:

`sqrt(15/36) = sqrt(15/6^2) = sqrt(15)/sqrt(6^2) = sqrt(15)/6`