Question

rationalise the denominator 1/3-2√2

Answer 1

Given problem is $\frac{1}{3-2 \sqrt{2}}$

To rationalize, we multiply by conjugate of the denominator.

Conjugate is obtained by changing the sign of radical term

So conjugate of $3-2 \sqrt{2}$ is $3+2 \sqrt{2}$

Hence we multiply and divide by $3+2 \sqrt{2}$

$=\frac{1}{3-2 \sqrt{2}}* \frac{3+2 \sqrt{2}}{3+2 \sqrt{2}}$

$= \frac{3+2 \sqrt{2}}{(3-2 \sqrt{2})(3+2 \sqrt{2})}$

$= \frac{3+2 \sqrt{2}}{(3)^2-(2 \sqrt{2})^2}$

$= \frac{3+2 \sqrt{2}}{9-(4 *2)}$

$= \frac{3+2 \sqrt{2}}{9-8}$

$= \frac{3+2 \sqrt{2}}{1}$

$= 3+2 \sqrt{2}$

Hence final answer is $= 3+2 \sqrt{2}$.

Answer 2

Hope this helps you!:)