# How do you simplify sqrt(1 / 3) + sqrt( 1 / 12)?

May 19, 2016

As primary root$\text{ } \frac{\sqrt{3}}{2}$

All possible solution $\text{ } \pm \frac{\sqrt{3}}{2}$

#### Explanation:

When dealing with fractions it is quite often an advantage to make the denominators the same.

Multiply $\frac{1}{3}$ by 1 but in the form of $1 = \frac{4}{4}$

$\sqrt{\frac{1}{3} \times \frac{4}{4}} + \sqrt{\frac{1}{12}}$

$\sqrt{4 \times \frac{1}{12}} + \sqrt{\frac{1}{12}}$

$\left[\sqrt{4} \times \sqrt{\frac{1}{12}}\right] + \sqrt{\frac{1}{12}}$

$2 \sqrt{\frac{1}{12}} + \sqrt{\frac{1}{12}}$

$3 \sqrt{\frac{1}{12}}$
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But it is not considered good form to have a root as the denominator.

Write as $\frac{3 \sqrt{1}}{\sqrt{12}}$

Multiply by 1 but in the form of $1 = \frac{\sqrt{12}}{\sqrt{12}}$

$\frac{3 \sqrt{12}}{12} = \frac{\sqrt{12}}{4}$

But 12 is $3 \times 4$ giving

$\frac{2 \sqrt{3}}{4} = \frac{\sqrt{3}}{2}$