Question

rationalize the denominator


√5-√3/√5+√3

Answer 1

√5-√3/√5+√3
= (√5-√3)(√5-√3)/(√5-√3)√5+√3)
= √5²+√3²-2(√5)(√3) / √5²-√3²
= 5+3-2√15/5-3
= 8 - 2√15 / 2
= 2(4-√15)/2
= 4-√15


here is ur answer

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Answer 2

$\displaystyle \sf{ \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } } = 4 - \sqrt{15}$

Given :

$\displaystyle \sf{ \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } }$

To find :

To rationalize the denominator

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } }$

Step 2 of 2 :

Rationalize the denominator

$\displaystyle \sf{ \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } }$

Multiplying both of the numerator and denominator by √5 - √3 we get

$\displaystyle \sf{ \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } }$

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

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

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

$\displaystyle \sf{ = \frac{ 5 - 2 \sqrt{15} + 3 }{ 2} }$

$\displaystyle \sf{ = \frac{ 8- 2 \sqrt{15} }{ 2} }$

$\displaystyle \sf{ = \frac{ 2(4 - \sqrt{15} ) }{ 2} }$

$\displaystyle \sf{ = 4 - \sqrt{15} }$

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