Question

rationalize the denominator
2÷√3-√5​

Answer 1

Answer:

2÷√3-√5 = 2÷√3-√5 × √3+√5 / √3+√5

= 2 √3+2√5 ÷ -2

Answer 2

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

Given :

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

To find :

To rationalize the denominator

Solution :

Step 1 of 2 :

Write down the given fraction

Here the given fraction is

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

Step 2 of 2 :

Rationalize the denominator

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

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

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

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

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

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

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

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

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