Question

How do you simplify `sqrt12 +sqrt 27`?

Answer 1

`5sqrt(3)`

Explanation:

`sqrt(12)+sqrt(27)=sqrt(2^2*3)+sqrt(3^2*3)=2sqrt(3)+3sqrt(3)=5sqrt(3)`

Note that:

• If `a >= 0` then `sqrt(a^2) = a`

• If `a, b >= 0` then `sqrt(ab) = sqrt(a) sqrt(b)`

So if `a, b >= 0` then:

`sqrt(a^2 b) = sqrt(a^2)sqrt(b) = a sqrt(b)`