Question

evaluate √5+√2/√5-√2, given that√10=3.162​

Answer 1

HLO GUYS,.

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Identities used :

{(a + b)}^{2}  =  {a}^{2}  +  {b}^{2}  + 2ab \\ (a + b)(a - b) =  {a}^{2}  -  {b}^{2}  

Given,  

√10 = 3.162

Now,

\frac{ \sqrt{5} +  \sqrt{2}  }{ \sqrt{5}  -  \sqrt{2} }  \\  

On rationalizing the denominator we get,

=  \frac{ \sqrt{5}  +  \sqrt{2} }{ \sqrt{5}  -  \sqrt{2} }  \times  \frac{ \sqrt{5}  +  \sqrt{2} }{ \sqrt{5} +  \sqrt{2}  }  \\  \\  =  \frac{ {( \sqrt{5} )}^{2}  +  {( \sqrt{2} )}^{2}  + 2( \sqrt{5} )( \sqrt{2}) }{ {( \sqrt{5}) }^{2}  -  {( \sqrt{2} )}^{2} }  \\  \\  =  \frac{5 + 2 +  2\sqrt{10} }{5 - 2}  \\  \\  =  \frac{7 +2 \sqrt{10}  }{3}  \\  \\  =  \frac{7 + 2 \times 3.162}{3}  \\  \\  =  \frac{7 + 6.324}{3}  \\  \\  =  \frac{13.324}{3}  \\  \\  = 4.441 \: (approx)

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Answer 2

$\sqrt{5} + \sqrt{2} \div \sqrt{5} - \sqrt{2 } \\ = ({ \sqrt{5} + \sqrt{2} })^{2} \div 3 \\ = (5 + 2 + 2 \sqrt{10} ) \div 3 \\ (7 + 2 \times 3.162) \div 3 \\ = (7 + 6.324) \div 3 \\ = 13.324 \div 3 \\ = 4.441$

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