How do you simplify #\sqrt { 27} + 2\sqrt { 48}#?

1 Answer
John D.
May 21, 2017

#11sqrt3#

Explanation:

First, factor everything inside the square roots into its prime factors.

The prime factorization of #27# is #3times3times3#
The prime factorization of #48# is #2 times 2 times 2 times 2 times 3#

Now, replace the numbers with these factors.

#sqrt(3times3times3) + 2sqrt(2times2times2times2times3)#

Next, identify pairs of factors inside the square root and pull them out.

#sqrt(color(orange)3timescolor(orange)3times3) + 2sqrt(color(blue)2timescolor(blue)2timescolor(red)2timescolor(red)2times3)#

#color(orange)3sqrt3 + 2(color(blue)2)(color(red)2)sqrt3#

Finally, simplify.

#3sqrt3 + 8 sqrt 3#

#11sqrt3#

Final Answer

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