How do you simplify #4sqrt(52x)+sqrt(117x)-2sqrt13#?

1 Answer
Feb 15, 2017

Answer:

#=sqrt13(8sqrtx +3sqrtx-2)#

Explanation:

Write each value under the root as the product of the factors, then we can compare the terms.

#4sqrt(52x) + sqrt(117x) - 2sqrt13#

#=4sqrt(4xx13x) + sqrt(9xx13x) - 2sqrt13#

#=4sqrt4xxsqrt(13x) + sqrt9xxsqrt(13x) - 2sqrt13#

#=4 xx 2 color(red)(sqrt13)sqrtx +3color(red)(sqrt13)sqrtx-2color(red)(sqrt13)" "larr# common factor

#=color(red)(sqrt13)(8sqrtx +3sqrtx-2)#