How do you simplify #(2sqrt(4x^2 + 36x + 81) + 3sqrt(9x^2 - 24xy + 16y^2))(2sqrt(x))#? Thanks in advance.

1 Answer
EZ as pi
Aug 14, 2016

#2sqrtx(13x-12y +18)#

Explanation:

#(2sqrt(4x^2 + 36x + 81) + 3sqrt(9x^2 - 24xy + 16y^2))(2sqrt(x))#

At first glance it seems that we can't simplify. However, finding the prime factors under a root sign is always a good start.
Notice that,4, 81, 9 and 16 are all perfect squares.

The expressions under the square roots are both perfect squares.

=#(2sqrt((2x+9))^2 + 3sqrt((3x-4y))^2)(2sqrt(x))#

=#(2(2x+9) + 3(3x-4y))2sqrtx#

=#(4x +18 +9x -12y)2sqrtx)#

=#(13x-12y+18)2sqrtx#

=#2sqrtx(13x-12y +18)#

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