How do you simplify #sqrt 6 + sqrt24#?

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Answer 1 · 2016-05-27T06:25:19

#3sqrt(6)#

Look at the prime factorisations of #6# and #24#:

#6 = 2 xx 3#

#24 = 2 xx 2 xx 2 xx 3 = 2^2*6#

Since #6# contains no square factors, #sqrt(6)# cannot be simplified.

Since #24# has a square factor #2^2#, we can simplify #sqrt(24)#:

#sqrt(24) = sqrt(2^2*6) = sqrt(2^2)*sqrt(6) = 2sqrt(6)#

Then:

#sqrt(6)+sqrt(24) = sqrt(6)+2sqrt(6) = 3sqrt(6)#