Question

Rationalize the denominator of the given question (in attachment) .. As fast as possible​

Answer 1

5(√3 -√2)

Step-by-step explanation:

$\frac{5}{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{\sqrt{2} - \sqrt{3} }$

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

$\frac{5( \sqrt{2} - \sqrt{3} )}{ - 1} = - 5( \sqrt{2} - \sqrt{3} )$

= -5√2 + 5√3

= 5√3 - 5√2

= 5(√3 -√2)

Answer 2

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$\frac{5}{ \sqrt{2} + \sqrt{3} } \\ \\ \frac{5}{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } \\ \\ = \frac{5( \sqrt{2} - \sqrt{3)} }{2 - 1} \\ \\ = - 5( \sqrt{2+3} )=5(√3-√2)$

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