Question

rationalized the denominator of(digit in pic)
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Answer 1

Step-by-step explanation:

to rationalise the denominator we should multiply and divide by the same denominator with changed sign. ie

$\frac{1}{ \sqrt{5} + \sqrt{2} } = \frac{1}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} }$

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

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

$= \frac{ \sqrt{5} - \sqrt{2} }{5 - 2}$

$= \frac{ \sqrt{5} - \sqrt{2} }{3}$