# How do you rationalize sqrt(12/147)?

May 13, 2015

$\sqrt{\frac{12}{147}} = \sqrt{\frac{\cancel{3} \cdot 4}{\cancel{3} \cdot 49}}$

$= \sqrt{\frac{4}{49}}$

We know that color(blue)(sqrt(a/b) = sqrta/sqrtb

Hence $\sqrt{\frac{4}{49}} = \frac{\sqrt{4}}{\sqrt{49}}$

 = color(green)(2/7

As the denominator 7 is a Rational Number, we can say that we have rationalised $\sqrt{\frac{12}{147}}$