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Rationalise the denominators of each of the following:$ \frac{3 \sqrt{2}}{\sqrt{5}} $
Given:
\( \frac{3\sqrt{2}}{\sqrt{5}} \)To do:
We have to rationalise the denominator of the given expression.
Solution:
We know that,
Rationalising factor of a fraction with denominator ${\sqrt{a}}$ is ${\sqrt{a}}$.
Rationalising factor of a fraction with denominator ${\sqrt{a}-\sqrt{b}}$ is ${\sqrt{a}+\sqrt{b}}$.
Rationalising factor of a fraction with denominator ${\sqrt{a}+\sqrt{b}}$ is ${\sqrt{a}-\sqrt{b}}$.
Therefore,
$\frac{3\sqrt{2}}{\sqrt{5}}=\frac{3\sqrt{2}}{\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}$
$=\frac{3\sqrt{2\times5}}{(\sqrt{5})^2}$
$=\frac{3\sqrt{10}}{5}$.
Hence, $\frac{3\sqrt{2}}{\sqrt{5}}=\frac{3\sqrt{10}}{5}$.
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