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

1 Answer
Jul 29, 2016

Answer:

#-4sqrt(26)#

Explanation:

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)#