Question

Rationalize the denominator:- a) 6 ÷ (√5 + √3)
b) 1 ÷ (√5 - 2)

Answer 1

Answer: hope the following images help...

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Answer 2

Question :-

Rationalize the Denominator :-

a) $\bold {\frac{6}{\sqrt{5} + \sqrt{3}} }$     b) $\bold {\frac{1}{\sqrt{5} - 2} }$

Solution :-

a) $\bold {\frac{6}{\sqrt{5} + \sqrt{3}} }$

Rationalising Factor = (√5 - √3)

$\begin {aligned} \implies \bold {\frac{6}{\sqrt{5} + \sqrt{3}}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} & = \frac{6 (\sqrt{5} - \sqrt{3})}{(\sqrt{5})^2 - (\sqrt{3})^2} \\\\\\ & \Rightarrow \frac{6 (\sqrt{5} - \sqrt{3})}{5 - 3} \\\\\\ & \Rightarrow \frac{6 (\sqrt{5} - \sqrt{3})}{2} & = \bold {3 (\sqrt{5} - \sqrt{3})} \end {aligned}$

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b) $\bold {\frac{1}{\sqrt{5} - 2} }$

Rationalizing Factor = (√5 + 2)

$\begin {aligned} \implies \bold {\frac{1}{\sqrt{5} - 2}} \times \frac{\sqrt{5} + 2}{\sqrt{5} + 2} & = \frac{\sqrt{5} + 2}{(\sqrt{5})^2 - 2^2} \\\\\\& \Rightarrow \frac{\sqrt{5} + 2}{5 - 4} \\\\\\& \Rightarrow \frac{\sqrt{5} + 2}{1} = \bold {\sqrt{5} + 2} \end {aligned}$

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