How do you simplify $((sqrt 2) + 2 (sqrt 2) + (sqrt8)) / (sqrt 3)$ ?

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Answer 1 · 2016-05-04T12:47:11

$(5sqrt(6))/3$

Consider $sqrt(8) -> sqrt(2xx2^2)=2sqrt(2)$

Write the given expression as:

$(sqrt(2)+2sqrt(2)+2sqrt(2))/sqrt(3)$

$(5sqrt(2))/sqrt(3)$

But it is not 'good form' to have a root in the denominator. So we need 'get rid' of it if we can.

Multiply by 1 but in the form of $1=sqrt(3)/sqrt(3)$

$(5sqrt(2))/sqrt(3)xxsqrt(3)/sqrt(3) = (5sqrt(6))/3$

'~~~~~~~~~~~~~~~~~~~~~~
Note that $sqrt(2)xxsqrt(3)=sqrt(2xx3)=sqrt(6)$

How do you simplify ((sqrt 2) + 2 (sqrt 2) + (sqrt8)) / (sqrt 3)((sqrt 2) + 2 (sqrt 2) + (sqrt8)) / (sqrt 3)?