Question

Simplify the following:

`8sqrt(3) - 3sqrt(27) + 6/sqrt(3)`

Answer 1

`8sqrt(3) - 3sqrt(27) + 6/sqrt(3)`

Step 1: Simplify each radical term

`sqrt(27) = sqrt(9 xx 3) = 3sqrt(3)`

So, `-3sqrt(27) = -3(3sqrt(3)) = -9sqrt(3)`

`6/sqrt(3) = 6/sqrt(3) xx sqrt(3)/sqrt(3) = (6sqrt(3))/3 = 2sqrt(3)`

Step 2: Substitute back

`8sqrt(3) - 9sqrt(3) + 2sqrt(3)`

Step 3: Combine like terms

`(8 - 9 + 2)sqrt(3) = 1/sqrt(3)`