Question

How do you simplify 2√12 - 7√3?

Answer 1

`-3sqrt(3)`

Explanation:

First of all, recall the following rule for non-negative real numbers `a` and `b`:
(1) `sqrt(a*b) = sqrt(a)*sqrt(b)`
For those who need a proof of this, just raise the right side to the power of `2` getting the expression under a square root on the left:
`(sqrt(a)*sqrt(b))^2 = sqrt(a)*sqrt(b)*sqrt(a)*sqrt(b) =`
`= sqrt(a)*sqrt(a)*sqrt(b)*sqrt(b) = a*b`,
which proves the property (1) above.

Using this property (1),
`2sqrt(12)-7sqrt(3) = 2sqrt(4*3) - 7sqrt(3) =`
`= 2sqrt(4)*sqrt(3) - 7sqrt(3) = 4sqrt(3) - 7sqrt(3) = -3sqrt(3)`