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

May 4, 2016

$\frac{5 \sqrt{6}}{3}$

#### Explanation:

Consider $\sqrt{8} \to \sqrt{2 \times {2}^{2}} = 2 \sqrt{2}$

Write the given expression as:

$\frac{\sqrt{2} + 2 \sqrt{2} + 2 \sqrt{2}}{\sqrt{3}}$

$\frac{5 \sqrt{2}}{\sqrt{3}}$

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 $1 = \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{5 \sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{5 \sqrt{6}}{3}$

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Note that $\sqrt{2} \times \sqrt{3} = \sqrt{2 \times 3} = \sqrt{6}$