Question

How do you simplify `sqrt12 / sqrt5`?

Answer 1

See a solution process below:

Explanation:

First, we can rationalize the denominator by multiplying the the fraction by the appropriate form of `1`:

`sqrt(5)/sqrt(5) * sqrt(12)/sqrt(5) =>`

`(sqrt(5) * sqrt(12))/(sqrt(5) * sqrt(5)) =>`

`sqrt(5 * 12)/5 =>`

`sqrt(60)/5`

Next, we can simplify the numerator as follows:

`sqrt(60)/5 =>`

`sqrt(4 * 15)/5 =>`

`(sqrt(4) * sqrt(15))/5 =>`

`(2sqrt(15))/5`

Answer 2

`(2sqrt15)/5`

Explanation:

First, multiply the numerator and denominator by `sqrt5`, which will get rid of the radical in the denominator. This is essentially the same as multiplying the expression by `1`.

`sqrt12/sqrt5 * color(blue)(sqrt5/sqrt5)`

`sqrt5 * sqrt 5 = sqrt25 = 5`, so the denominator becomes `5`. Similarly, `sqrt12 * sqrt 5 = sqrt60`.

`=sqrt60/5`

Now, we can split `sqrt60` into `sqrt4*sqrt15`.

`=(sqrt4*sqrt15)/5`

`=(2sqrt15)/5`