How do you simplify (square root 2) + 2 (square root 2) + (square root 8) / (square root 3)?

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How do you simplify (square root 2) + 2 (square root 2) + (square root 8) / (square root 3)?

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Answer 1 · 2015-09-06T23:06:46

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

Explanation:

I'll assume that the expression looks like this

$\frac{\sqrt{2} + 2 \sqrt{2} + \sqrt{8}}{\sqrt{3}}$ $(sqrt(2) + 2sqrt(2) + sqrt(8))/sqrt(3)$

Start by focusing on the numerator. More specifically, notice that you can rewrite $\sqrt{8}$ $sqrt(8)$ as

$\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2 \cdot \sqrt{2}$ $sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2 * sqrt(2)$

The numerator will then take the form

$\sqrt{2} + 2 \sqrt{2} + 2 \sqrt{2} = 5 \sqrt{2}$ $sqrt(2) + 2 sqrt(2) + 2sqrt(2) = 5sqrt(2)$

Next, you need to rationalize the denominator. To do that, multiply the fraction by $1 = \frac{\sqrt{3}}{\sqrt{3}}$ $1 = sqrt(3)/sqrt(3)$

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

The final form of the expression will be

$\frac{5 \cdot \sqrt{6}}{\sqrt{3^{2}}} = \frac{5}{3} \cdot \sqrt{6}$ $(5 * sqrt(6))/sqrt(3^2) = color(green)(5/3 * sqrt(6))$

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How do you simplify (square root 2) + 2 (square root 2) + (square root 8) / (square root 3)?

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