Question

solve
$\frac{3}{ \sqrt{5} - \sqrt{3} }$
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Answer 1

Solution :-

$: \implies\bold{\dfrac{3}{ \sqrt{5} - \sqrt{3}}}$

$: \implies\bold{\dfrac{3 \times \sqrt{5} + \sqrt{3}}{ \sqrt{5} - \sqrt{3} \times \sqrt{5} + \sqrt{3}}}$

$: \implies\bold{\dfrac{3 \times \sqrt{5} + \sqrt{3}}{ \big(\sqrt{5} \big)^{2} - \big( \sqrt{3} \big) \: ^{2} }}$

$: \implies\bold{\dfrac{3\sqrt{5} + 3\sqrt{3}}{ 5 - 3}}$

$: \implies\bold{\dfrac{3\sqrt{5} + 3\sqrt{3}}{2}}$

$\boxed{\sf\red{\dfrac{3\sqrt{5} + 3\sqrt{3}}{2}}}$

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Know more :-

Some identities --

• $\sf{(a + b)^2 = a^2 + b^2 + 2ab}$
• $\sf{(a - b)^2 = a^2 + b^2 - 2ab}$
• $\sf{(a - b)^3 = a^3 - b^3 - 3ab(a - b)}$
• $\sf{(a + b)^3 = a^3 + b^3 + 3ab(a + b)}$