Question

$1 \div 3 \sqrt{5}$
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Answer 1

Answer:

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Answer 2

${\texttt{\huge{\blue{solution}}}}$

For solving this firstly we will multiply and divide this denominator with its conjugate...

$\frac{1}{3 + \sqrt{5} } = \frac{1}{3 + \sqrt{5} } \times \frac{3 - \sqrt{5} }{3 - \sqrt{5} }$

$\frac{1}{3 + \sqrt{5} } = \frac{3 - \sqrt{5} }{(3 - \sqrt{5} )(3 + \sqrt{5} )}$

Now, using the formulae...

${a}^{2} - {b}^{2} = (a + b)(a - b)$

It will be...

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

$\frac{1}{3 + \sqrt{5} } = \frac{3 - \sqrt{5} }{9 - 5}$

$\frac{1}{3 + \sqrt{5} } = \frac{3 - \sqrt{5} }{4}$

$\frac{1}{3 + \sqrt{5} } = \frac{3}{4} - \frac{ \sqrt{5} }{4}$

Answer...

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