Simplify each of the following by rationalising the denominator:
$\frac{1}{3 \sqrt{2} - 2 \sqrt{3}}$

Open in App

Solution

$\frac{1}{3 \sqrt{2} - 2 \sqrt{3}}$
Multiply by $3 \sqrt{2} + 2 \sqrt{3}$ numerator and denominator we get
$= \frac{1 (3 \sqrt{2} + 2 \sqrt{3})}{(3 \sqrt{2} - 2 \sqrt{3}) (3 \sqrt{2} + 2 \sqrt{3})}$
$= \frac{3 \sqrt{2} + 2 \sqrt{3}}{(3 \sqrt{2})^{2} - (2 \sqrt{3})^{2}}$
$= \frac{3 \sqrt{2} + 2 \sqrt{3}}{18 - 12}$
$= \frac{3 \sqrt{2} + 3 \sqrt{2}}{6}$

Suggest Corrections

Similar questions

Simplify of the following by rationalizing the denominator:
$\frac{6 - 4 \sqrt{2}}{6 + 4 \sqrt{2}}$

Simplify $\frac{1}{2 - \sqrt{7}}$ by rationalising the denominator.

\frac{6 - 4 \sqrt{3}}{6 + 4 \sqrt{3}}

4 \sqrt{\frac{1}{3}} + \frac{1}{2} \sqrt{48}

\frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} + \sqrt{5}}

Join BYJU'S Learning Program