After rationalising the denominator of $ \frac{3 \sqrt{2}}{3 \sqrt{2}-2 \sqrt{2}} $, we get the denominator as

Given:

\( \frac{3 \sqrt{2}}{3 \sqrt{2}-2 \sqrt{2}} \)

To do:

We have to find the denominator after rationalisation.
Solution:
 We know that,

Rationalising factor of a fraction of denominator $a-\sqrt{b}$ is $a-\sqrt{b}$.

Therefore,

$\frac{3 \sqrt{2}}{3 \sqrt{2}-2 \sqrt{2}}=\frac{3 \sqrt{2}}{3 \sqrt{2}-2 \sqrt{2}}\times\frac{3 \sqrt{2}+2 \sqrt{2}}{3 \sqrt{2}+2 \sqrt{2}}$

$=\frac{3\sqrt2(5\sqrt2)}{(3\sqrt2)^2-(2\sqrt2)^2}$

$=\frac{15\times2}{18-8}$

$=\frac{30}{10}$

$=3$

The denominator after rationalising is 10.

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Updated on: 10-Oct-2022

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