How do you simplify #24/sqrt(3)#?

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Answer 1 · 2016-08-01T11:31:06

#8 * sqrt(3)#

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)#