Question

fill in blank the value of 2 upon √5-√3 is equal to​

Answer 1

Question :-

what is the value of $\dfrac{2}{ \sqrt{5} - \sqrt{3} }$

Solution :-

rationalize the denominator we get the value :-

$\red \implies \dfrac{2}{ \sqrt{5} - \sqrt{3} } \\ \\ \implies \dfrac{2}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{\sqrt{5} + \sqrt{3}} \\ \\ \implies \: \frac{2 (\sqrt{5} + \sqrt{3} )}{ { (\sqrt{5}) }^{2} - {( \sqrt{3}) }^{2} } \\ \\ \implies \: \frac{2( \sqrt{5} + \sqrt{3}) }{5 - 3} \\ \\ \implies \: \frac{2( \sqrt{5} + \sqrt{3}) }{2} \\ \\ \implies \: \frac{\cancel2( \sqrt{5} + \sqrt{3}) }{ \cancel2} \\ \\ \implies \: \sqrt{5} + \sqrt{3}$

so the value of $\dfrac{2}{ \sqrt{5} - \sqrt{3} }$ = √5 + √3 .

Answer 2

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$\green{\bold{\underline{\underline{Question}}}}$

$\frac{2}{√5-√3 }$ = ?

$\huge\star\underbrace{\mathtt\red{A} \mathtt\red{n} \mathtt\red{s} \mathtt\red{w} \mathtt\red{e} \mathtt\red{r}} \star\:$

$\frac{2}{√5-√3 }$

= $\frac{2(√5+√3)}{(√5-√3)(√5+√3)}$

= $\frac{2(√5+√3)}{(√5)²-(√3)²}$

= $\frac{2(√5+√3)}{ 5-3}$

= $\frac{2(√5+√3)}{2}$

=$√5+√3$

❥→ . ' . $\frac{2}{√5-√3 }$ = $√5+√3$

____________________________

Formula used:

➛

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