How do you simplify $\sqrt{2 x} \div \sqrt{9 x}$ $sqrt(2x ) div sqrt(9x)$ ?

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How do you simplify $\sqrt{2 x} \div \sqrt{9 x}$ $sqrt(2x ) div sqrt(9x)$ ?

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Answer 1 · 2015-09-20T20:04:34

$\frac{\sqrt{2}}{3}$ $sqrt2/3$

Explanation:

Rewrite in fractional form:
$\sqrt{2 x} \div \sqrt{9 x} = \frac{\sqrt{2 x}}{\sqrt{9 x}}$ $sqrt(2x) -: sqrt(9x) = sqrt(2x)/sqrt(9x)$

Remember the rule:
$\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab)=sqrt(a)sqrt(b)$

so breaking down the roots, we get:
$= \frac{\sqrt{2} \sqrt{x}}{\sqrt{9} \sqrt{x}}$ $= (sqrt(2)sqrt(x))/(sqrt(9)sqrt(x))$

Now, $\frac{\sqrt{x}}{\sqrt{x}} = 1$ $sqrt(x)/sqrt(x)=1$ so that's gone, and $\sqrt{9} = 3$ $sqrt(9)=3$ , so we end up having:
$= \frac{\sqrt{2}}{3}$ $= sqrt2/3$

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How do you simplify $\sqrt{2 x} \div \sqrt{9 x}$ $sqrt(2x ) div sqrt(9x)$ ?

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