How do you simplify #sqrt 8 (sqrt 13 - sqrt 117)#?

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Answer 1 · 2016-07-29T13:22:57

#-4sqrt(26)#

Consider the factor tree of 117

Note that if the sum of the digits is exactly divisible by 3 then the whole number is also divisible by 3.

Tony B

So the prime number factors of 117 are #3^2xx13#

Given:#" "sqrt(8)(sqrt(13)-sqrt(117))#

Write as:

#sqrt(8)(sqrt(13)-3sqrt(13))#

Factor out #sqrt(13)# giving:

#sqrt(8)sqrt(13)(1-3)#

Note that # sqrt(8)=2sqrt(2)# giving:

#2sqrt(2)sqrt(13)xx(-2)#

#=>-4sqrt(2xx13) -> -4sqrt(26)#