Question

Write the value of 1\√5-√3

Answer 1

Answer:

$value \: of \: \frac{1}{ \sqrt{5} - \sqrt{3} }$

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

√5+√3

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5-3

√5+√3

= ------------ =ANSWER:-

2

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Answer 2

$Value \:of \: \frac{1}{(\sqrt{5} - \sqrt{3})}$

$Multiplying\: numerator\: and\: denominator\\ by\: (\sqrt{5} + \sqrt{3}) ,\:we \:get$

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

/* By Algebraic Identity */

$\boxed { \pink { (x + y)(x - y) = x^{2} - y^{2} }}$

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

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

Therefore.,

$\red{Value \:of \: \frac{1}{(\sqrt{5} - \sqrt{3})}}\green {= \frac{(\sqrt{5}+\sqrt{3})}{2}}$

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