Question

rationalise the following question
$1 \div 5 \sqrt{3} - 3 \sqrt{5}$
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Answer 1

Correct Statement :

Rationalise the following question :

$\sf \dfrac{1}{5 \sqrt{3} - 3 \sqrt{5} }$

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Solution :

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We have to rationalise :

• $\sf \dfrac{1}{5 \sqrt{3} - 3 \sqrt{5}}$

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Let's Rationalise :

$\sf \dfrac{1}{5 \sqrt{3} - 3 \sqrt{5}}$

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By Rationalisation :

$\sf : \implies \dfrac{1}{5 \sqrt{3} - 3 \sqrt{5}} \times \dfrac{5 \sqrt{3} + 3 \sqrt{5}}{5 \sqrt{3} + 3 \sqrt{5}}$

$\sf : \implies \dfrac{1 \times (5 \sqrt{3} + 3 \sqrt{5})}{(5 \sqrt{3} - 3 \sqrt{5})(5 \sqrt{3} + 3 \sqrt{5})}$

$\sf : \implies \dfrac{5 \sqrt{3} + 3 \sqrt{5}}{(5 \sqrt{3} - 3 \sqrt{5})(5 \sqrt{3} + 3 \sqrt{5})}$

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By using identinty :

$\large \underline{\boxed{\bf{(a-b)(a+b) = a^{2} - b^{2}}}}$

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

$\sf : \implies \dfrac{5 \sqrt{3} + 3 \sqrt{5}}{(25 \times 3) - (9 \times 5)}$

$\sf : \implies \dfrac{5 \sqrt{3} + 3 \sqrt{5}}{75 - 45}$

$\sf : \implies \dfrac{5 \sqrt{3} + 3 \sqrt{5}}{30}$

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Hence, Answer is :

$\large \underline{\boxed{\bf{\dfrac{5 \sqrt{3} + 3 \sqrt{5}}{30}}}}$