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)#