How do you simplify $\frac{(\sqrt{2}) + 2 (\sqrt{2}) + (\sqrt{8})}{\sqrt{3}}$ $((sqrt 2) + 2 (sqrt 2) + (sqrt8)) / (sqrt 3)$ ?

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Answer 1 · 2016-05-04T12:47:11

$\frac{5 \sqrt{6}}{3}$ $(5sqrt(6))/3$

Consider $\sqrt{8} \to \sqrt{2 \times 2^{2}} = 2 \sqrt{2}$ $sqrt(8) -> sqrt(2xx2^2)=2sqrt(2)$

Write the given expression as:

$\frac{\sqrt{2} + 2 \sqrt{2} + 2 \sqrt{2}}{\sqrt{3}}$ $(sqrt(2)+2sqrt(2)+2sqrt(2))/sqrt(3)$

$\frac{5 \sqrt{2}}{\sqrt{3}}$ $(5sqrt(2))/sqrt(3)$

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 $1 = \frac{\sqrt{3}}{\sqrt{3}}$ $1=sqrt(3)/sqrt(3)$

$\frac{5 \sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{5 \sqrt{6}}{3}$ $(5sqrt(2))/sqrt(3)xxsqrt(3)/sqrt(3) = (5sqrt(6))/3$

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Note that $\sqrt{2} \times \sqrt{3} = \sqrt{2 \times 3} = \sqrt{6}$ $sqrt(2)xxsqrt(3)=sqrt(2xx3)=sqrt(6)$

How do you simplify ((sqrt 2) + 2 (sqrt 2) + (sqrt8)) / (sqrt 3)(√2)+2(√2)+(√8)√3((sqrt 2) + 2 (sqrt 2) + (sqrt8)) / (sqrt 3)?