Question

Rationalize the denominator 1/root5+3

Answer 1

Question: Rationalise the denominator in $\dfrac {1}{\sqrt{5}+3}$

$\textbf {\underline {\underline {Solution:}}}$

$\dfrac {1}{\sqrt{5}+3}$ × $\dfrac {\sqrt {5}-3}{\sqrt {5}-3}$

= $\dfrac {1}{(\sqrt {5})^2-{(3)}^2}$

$\textbf {\underline {\underline {Identity: }}}$ ${a}^2 - {b}^2 = ( a + b) (a - b)$

= $\dfrac {\sqrt{5}-3}{5-9}$

${\boxed{\sf\:{Answer}}} =$$- \dfrac{\sqrt {5}-3}{4}$

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