Question

How do you simplify `sqrt(32/4)`?

Answer 1

`2sqrt2`

Explanation:

There are 2 solutions :)

The first solution is:

Since `sqrt(a/b) = sqrt(a)/sqrt(b)`, where `b` is not equal to `0`.

First we simplify the numerator, since there is no exact value of `sqrt32` we take its perfect squares. `16` is a perfect square since `4*4 = 16`. Dividing `32` by `16`, we get `16 * 2 = 32`, therefore:

`sqrt32 = sqrt16*sqrt2`
`= 4sqrt2`

Since now we're done in the numerator, we're gonna simplify the denominator, since `4` is perfect square, `4 = 2 * 2`, the `sqrt4` is equal to `2`.

Plugging all the answers, we get:

`(4sqrt2)/2`

since `4` and `2` is a whole number, we can divide these 2 whole numbers, we get:

`2sqrt2`

this is the final answer :)

the 2nd solution is:

First we simply evaluate the fraction inside the radical sign (square root)

`sqrt(32/4) = sqrt(8)`

since, `32/4` = `8`, then we get `sqrt8`

`sqrt8 = sqrt4*sqrt2`

`= 2sqrt2`