Question

rationalize 3/√5+√2​

Answer 1

$\underline{\underline{\orange{\textbf{Step - By - Step - Explanation : -}}}}$

• we need to Rationalize the denominator of 3/5+ √2.

For rationalizing the denominator we have to multiply the numerator and the denominator by denominator but we should change the sign.

If

• (+) into (-)
• (-) into (+)

$\sf \: = \frac{3}{ \sqrt{5} + \sqrt{2} } \\ \\ \sf \: = \frac{3}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ \\ \sf \: = \frac{3( \sqrt{5} - \sqrt{2}) }{( \sqrt{5} + \sqrt{2})( \sqrt{5} - \sqrt{2)} } \\ \\ \sf \: by \: using \: identity \: (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{3( \sqrt{5} - \sqrt{2}) }{ {( \sqrt{5}) }^{2} -( \sqrt{2} {)}^{2} } \\ \\ \sf \: = \frac{3( \sqrt{5} - \sqrt{2} ) }{5 - 2} \\ \\ \sf \: = \frac{ \cancel{3}( \sqrt{5} - \sqrt{2} )}{ \cancel3} \\ \\ \bf = \sqrt{5} - \sqrt{2}$

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