# `sqrt(45/32)` Simplify the expression.

## Expert Answers In order to simplify the radicals, we need to find factors of ` 45` and `32` that are perfect square numbers.

The perfect square numbers are: `4, 9, 16, 25, 36, 49, 64, 81, 100, .. `

The factor of` 45` that we could use is `9` , for the `32` we can use the 16.
`(sqrt(45))/(sqrt(32)) = (sqrt(9)*sqrt(5))/(sqrt(16)*sqrt(2))`

We know that` 3 * 3 = 9 ` and `4 * 4 = 16` , so `sqrt(9) = 3 and sqrt(16) = 4` .
`(sqrt(9)*sqrt(5))/(sqrt(16)*sqrt(2)) = (3sqrt(5))/(4sqrt(2))`

There is a radical expression at the bottom, so we will multiply top and bottom by `sqrt(2)` .
`(3sqrt(5)*sqrt(2))/(4sqrt(2)*sqrt(2)) = (3sqrt(10))/(4sqrt(4)) `

We know that `2 * 2 = 4` , so `sqrt(4) = 2` .
`(3sqrt(10))/(4sqrt(4)) = (3sqrt(10))/(4*2) = (3sqrt(10))/8`

Therefore, `(sqrt(45))/(sqrt(32)) = (3sqrt(10))/8` .

That is it!

Approved by eNotes Editorial Team

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