Question

Rationalize the dinominator
a) 3/(√3-√2)+√5



Kindly don't answer,If you don't know the answer ​

Answer 1

Answer:

$\frac{- \sqrt{18} + \sqrt{12 } + \sqrt{30}}{4}$

Step-by-step explanation:

Question -

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

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Solution-

$\frac{3}{( \sqrt{3} - \sqrt{2}) + \sqrt{5} } \\ \\ = \frac{3}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \times \frac{( \sqrt{3} - \sqrt{2} )- \sqrt{5} }{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} } \\ \\ = \frac{3( \sqrt{3} - \sqrt{2} - \sqrt{5} ) }{( \sqrt{3} {)}^{2} + ( \sqrt{2} {)}^{2} - 2( \sqrt{3} \sqrt{2}) - ( \sqrt{5} {)}^{2} } \\ \\ = \frac{3( \sqrt{3} - \sqrt{2} - \sqrt{5} )}{3 + 2 - 2 \sqrt{6} - 5} \\ \\ = \frac{3( \sqrt{3} - \sqrt{2} - \sqrt{5}) }{ - 2 \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } \\ \\ = \frac{3( \sqrt{18} - \sqrt{12} - \sqrt{30} ) }{ - 12} \\ \\ = \frac{3( \sqrt{18} - \sqrt{12} - \sqrt{30} )}{3( - 4)} \\ \\ = \frac{ \sqrt{18} - \sqrt{12} - \sqrt{30} }{ - 4} \\ \\ = \frac{ - ( \sqrt{18} - \sqrt{12} - \sqrt{30}) }{4} \\ \\ = \frac{ - \sqrt{18} + \sqrt{12 } + \sqrt{30} }{4}$

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Required Answer -

$\color{lime}\bold\rightarrow$ $\tt\red{\frac{- \sqrt{18} + \sqrt{12 } + \sqrt{30} }{4}}$

Answer 2

Answer:

$\frac{3}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \\ \\ = \frac{3}{( \sqrt{3} - \sqrt{2}) + \sqrt{5} } \times \frac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ \sqrt{3} - \sqrt{2} - \sqrt{5} } \\ \\ = \frac{3 \sqrt{3} - 3 \sqrt{2} - 3 \sqrt{5} }{ {( \sqrt{3} - \sqrt{2} )}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{3 \sqrt{3} - 3 \sqrt{2} - 3 \sqrt{5} }{3 + 2 - 2 \sqrt{6} - 5} \\ \\ = \frac{3 \sqrt{3} - 3 \sqrt{2} - 3 \sqrt{5} }{ - 2 \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } \\ \\ = \frac{9 \sqrt{2} - 6 \sqrt{3} - 3 \sqrt{30} }{ - 12} \\ \\ = \frac{ \sqrt{30} + 2 \sqrt{3} - 3 \sqrt{2} }{4}$