# How do you simplify sqrt((1/18))?

Oct 30, 2015

$\frac{\sqrt{2}}{6}$

#### Explanation:

Since there can't be a square root (a radical) in the denominator, rationalize it by multiplying both the numerator and denominator with $\sqrt{2}$.

$\sqrt{\frac{1}{18}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

$= \sqrt{\frac{2}{36}}$

$= \frac{1}{6} \sqrt{2}$ or $\frac{\sqrt{2}}{6}$

You multiply by $\sqrt{2}$ in order to make the denominator $\sqrt{36}$ because $\sqrt{36} = 6$ and so you can take it out of the square root.

Oct 30, 2015

$\frac{\sqrt{2}}{6}$

#### Explanation:

It is a matter of splitting the numbers up into factors that have a root if you can. Then taking these outside of the root by applying that root.

What factors are there of 18 that we can apply a root to?
The obvious ones are 2 and 9 as $2 \times 9 = 18$ we can take the root of 9 but not of 2. So we end up with:

sqrt((1/18)) = sqrt(1/(2 times 9)

This can be split so that we have:

$\sqrt{\frac{1}{2} \times \frac{1}{9}} = \frac{1}{3} \sqrt{\frac{1}{2}}$

But convention is that you do not have a root as a denominator if you can help it.

Write as: $\frac{1}{3} \frac{\sqrt{1}}{\sqrt{2}}$ This does work. Check it on a calculator.

But $\sqrt{1} = 1$ giving:

$\frac{1}{3} \times \frac{1}{\sqrt{2}}$

To 'get rid' of the root in the denominator multiply by the value 1 (does not change the overall values) but write the 1 in the form of $\frac{\sqrt{2}}{\sqrt{2}}$ giving:

$\frac{1}{3} \times \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

But $\sqrt{2} \times \sqrt{2} = 2$

So now we have:
$\frac{1}{3} \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{6}$

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