Question

Simplify: `(2sqrt(27) + 3sqrt(12))/(4sqrt(3))`.

Answer 1

Given: `(2sqrt(27) + 3sqrt(12))/(4sqrt(3))`

Step-wise calculation:

1. `sqrt(27) = sqrt(9 xx 3)` 

= `3sqrt(3)` 

`sqrt(12) = sqrt(4 xx 3)` 

= `2sqrt(3)`

2. Numerator = `2 xx (3sqrt(3)) + 3 xx (2sqrt(3))` 

= `6sqrt(3) + 6sqrt(3)` 

= `12sqrt(3)`

3. Expression = `(12sqrt(3))/(4sqrt(3))` 

= `12/4`

= 3