How do you simplify 2√12 - 7√3?

1 Answer
Oct 1, 2015

Answer:

#-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)#