Question

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

Answer 1

`sqrt(1/3) = sqrt(3)/3`

Explanation:

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.