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

$(8 * color(red)(cancel(color(black)(3))) * sqrt(3))/color(red)(cancel(color(black)(3))) = 8 * sqrt(3)$

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