Question

How do you simplify `4 *sqrt(3/4)`?

Answer 1

`color(crimson)( => 2 sqrt 3`

Explanation:

`4 * sqrt(3/4)`

`=> (sqrt 4)^2 * sqrt 3 / sqrt 4`

`=> sqrt 4 * cancel (sqrt 4) * sqrt 3 / cancel sqrt 4`

`=> sqrt 4 * sqrt 3`

`color(crimson)( => 2 sqrt 3`

Answer 2

`2sqrt3`

Explanation:

`4 cdot sqrt(3/4)`

`4 cdot sqrt3/sqrt4`

`4 cdot sqrt3/sqrt4 xx sqrt4/sqrt4`

`4 cdot (sqrt3 xx sqrt4)/(sqrt4 xx sqrt4)`

`4 cdot sqrt12/4`

`cancel4 cdot sqrt12/cancel4`

`sqrt12`

`sqrt(3 xx 4)`

`sqrt3 xx sqrt4`

`sqrt3 xx 2`

`2sqrt3`

Answer 3

`color(blue)(=> 2 sqrt3`

Explanation:

`4 * sqrt (3/4)`

`=> 4 * sqrt 3 / sqrt 4`

`=>cancel(4)^color(red)(2) * sqrt 3 / cancel2`

`color(blue)(=> 2 sqrt3`

Answer 4

`2sqrt3`

Explanation:

The key realization is that we can rewrite `sqrt(3/4)` as `sqrt3/sqrt4`. We now have

`4*sqrt3/sqrt4`

This simplifies to

`4*sqrt3/2`

Cancelling out common factors

`cancel(4)^2*sqrt3/cancel2`

`=>2sqrt3`

Hope this helps!