Question

$rationalise \: the \: denominator \: \\ \frac{1}{ \sqrt{7 - \sqrt{6} } }$
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Answer 1

$\sf\huge\orange{\underbrace{ Solution : }}$

$\sf \implies \cfrac{1}{\sqrt{7} - \sqrt{6}}$

• Multiply both numerator and denominator with √7 + √6.

$\sf \implies \cfrac{1}{\sqrt{7} - \sqrt{6}} \times \cfrac{\sqrt{7}+ \sqrt{6}}{\sqrt{7}+ \sqrt{6}}$

$\sf \implies \cfrac{\sqrt{7} + \sqrt{6}}{(\sqrt{7}-\sqrt{6})(\sqrt{7} + \sqrt{6})}$

• (a - b)(a + b) = a² - b²

$\sf \implies \cfrac{\sqrt{7}+\sqrt{6}}{(\sqrt{7})^{2} - (\sqrt{6})^{2}}$

$\sf \implies \cfrac{\sqrt{7}+\sqrt{6}}{7-6}$

$\sf \implies \sqrt{7}+\sqrt{6}$

$\underline{\boxed{\rm{\purple{\therefore \cfrac{1}{\sqrt{7} - \sqrt{6}} = \sqrt{7}+\sqrt{6}.}}}}\:\orange{\bigstar}$