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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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