Rajasthan 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 $(\sqrt{3}+\sqrt{5}).$
$y=\frac{5}{\sqrt{3}-\sqrt{5}} \times \frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}+\sqrt{5}} [$by rationalising$]$
$=\frac{5(\sqrt{3}+\sqrt{5})}{(\sqrt{3})^{2}-(\sqrt{5})^{2}} [\because (a-b)(a+b)=a^{2 }- b^2]$
$=\frac{5(\sqrt{3}+\sqrt{5})}{3-5}$
$=-\frac{5}{2}(\sqrt{3}+\sqrt{5})$
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