How do you simplify #24/sqrt(3)#?
1 Answer
Aug 1, 2016
Explanation:
Your first goal here will be to rationalize the denominator by multiplying the fraction by
#1 = sqrt(3)/sqrt(3)#
This will allow you to remove the radical term from the denominator, since
#sqrt(3) * sqrt(3) = sqrt(3 * 3) = sqrt(3^2) = 3#
You thus have
#24/sqrt(3) * sqrt(3)/sqrt(3) = (24 * sqrt(3))/(sqrt(3) * sqrt(3)) = (24 * sqrt(3))/3#
One last thing to do here -- simplify the resulting fraction by using the fact that
#24 = 12 * 2 = 6 * 2 * 2 = 2 * 2 * 2 * 3 = 2^3 * 3 = 8 * 3#
Your final answer will be
#(8 * color(red)(cancel(color(black)(3))) * sqrt(3))/color(red)(cancel(color(black)(3))) = 8 * sqrt(3)#