How do you add $sqrt24 + sqrt54$ ?

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Answer 1 · 2015-04-04T17:50:30

The answer is $5sqrt(6)$

In this type of problems, there is a rule zero: Prime Factorization.

$24=2^3 *3$ and $54 = 3^3 *2$

So

$sqrt(24) + sqrt(54) = sqrt(2^3*3) + sqrt(3^3*2)$

$= sqrt(2^2*2*3) + sqrt(3^2*3*2)$

$=2sqrt(2*3)+3sqrt(3*2)$

$2sqrt(6)+3sqrt(6) = sqrt(6)(2+3) = 5sqrt(6)$

How do you add sqrt24 + sqrt54sqrt24 + sqrt54?