How do you simplify 24/sqrt(3)24√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)1=√3√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√3⋅√3=√3⋅3=√32=3
You thus have
24/sqrt(3) * sqrt(3)/sqrt(3) = (24 * sqrt(3))/(sqrt(3) * sqrt(3)) = (24 * sqrt(3))/324√3⋅√3√3=24⋅√3√3⋅√3=24⋅√33
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 * 324=12⋅2=6⋅2⋅2=2⋅2⋅2⋅3=23⋅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)
