How do you rationalize the denominator and simplify $\sqrt{\frac{1}{3}}$ $sqrt (1 / 3)$ ?

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How do you rationalize the denominator and simplify $\sqrt{\frac{1}{3}}$ $sqrt (1 / 3)$ ?

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Answer 1 · 2016-12-23T13:06:00

$\sqrt{\frac{1}{3}} = \frac{\sqrt{3}}{3}$ $sqrt(1/3) = sqrt(3)/3$

Explanation:

If $a, b > 0$ $a, b > 0$ then $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b) = sqrt(a)/sqrt(b)$

So we find:

$\sqrt{\frac{1}{3}} = \sqrt{\frac{3}{9}} = \sqrt{\frac{3}{3^{2}}} = \frac{\sqrt{3}}{\sqrt{3^{2}}} = \frac{\sqrt{3}}{3}$ $sqrt(1/3) = sqrt(3/9) = sqrt(3/3^2) = sqrt(3)/sqrt(3^2) = sqrt(3)/3$

The trick is to make the denominator of a fraction into a perfect square before you take the square root.

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How do you rationalize the denominator and simplify $\sqrt{\frac{1}{3}}$ $sqrt (1 / 3)$ ?

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