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

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Answer 1 · 2016-12-23T13:06:00

$sqrt(1/3) = sqrt(3)/3$

If $a, b > 0$ then $sqrt(a/b) = sqrt(a)/sqrt(b)$

So we find:

$sqrt(1/3) = sqrt(3/9) = sqrt(3/3^2) = sqrt(3)/sqrt(3^2) = sqrt(3)/3$

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

How do you rationalize the denominator and simplify sqrt (1 / 3)sqrt (1 / 3)?