Question

Simplify √5-√3÷√5+√3
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Answer 1

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Simplify √5-√3÷√5+√3

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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$= > \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

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

=>denominator is in the form of (a+b)(a-b)

so ,here this identity is used:-

$\bold{\boxed{ = > (a + b)(a - b) = {a}^{2} - {b}^{2} }}$

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

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

$= > \frac{5 + 3 - 2 \sqrt{5} \sqrt{3} }{2}$

Taking 2 as common from numerator

$= > \frac{8 - 2 \sqrt{5} \sqrt{3} }{2}$

=>cancel 2 from both Numerator and denominator.

$= > \frac{2(4 - \sqrt{5} \sqrt{3}) }{2} = \bold{\red{4 - \sqrt{5} \sqrt{3} }}$(Answer)

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