Gujarat BoardEnglish MediumSTD 9MathsNumber systems2 Marks
Question
Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$
✓
Answer
Let $y=\frac{5}{\sqrt{3}-\sqrt{5}}$ and its denominator $=\sqrt{3}-\sqrt{5}$
Here, the conjugate of denominator $(\sqrt{3}-\sqrt{5})$ is $(\sqrt{3}+\sqrt{5})$.
$y=\frac{5}{\sqrt{3} \sqrt{5}} \times \frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}+\sqrt{5}}[\text { by rationalising })$
$=\frac{5(\sqrt{3}+\sqrt{5})}{(\sqrt{3})^2-(\sqrt{5})^2}\left[\because(a-b)(a+b)=a^2-b^2\right]$
$=\frac{5(\sqrt{3}+\sqrt{5})}{3-5}=-\frac{5}{2}(\sqrt{3}+\sqrt{5})$
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