Question

Question #1eeb2

Answer 1

`2sqrt(3)`

Explanation:

In this format the brackets do not do anything so disregard them.

`15/sqrt(3)-sqrt(27)`

Mathematicians do not like roots in the denominator so lets 'get rid' of it. Multiply by 1 and you do not change a value. However, 1 comes in many forms so you can change the way something looks without changing its intrinsic value.

`color(green)([15/sqrt(3)color(red)(xx1)]-sqrt(27)`

`color(green)([15/sqrt(3)color(red)(xxsqrt(3)/sqrt(3))]-sqrt(27)`

`color(green)([(15sqrt(3))/3]-sqrt(27))`

But `sqrt(27) = sqrt(3xx9)=sqrt(3xx3^2)=3sqrt(3)`

`(15sqrt(3))/3-3sqrt(3)`

Factor out the `sqrt(3)`

`sqrt(3)xx[15/3-3]`

`sqrt(3)xx6/3`

`2sqrt(3)`