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:

$2sqrt(2)sqrt(13)xx(-2)$

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

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