Question

6 upon under root 5 + under root 2

Answer 1

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

Answer 2

$\frac{6}{ \sqrt{5}+ \sqrt{2} }$
⇒$\frac{6( \sqrt{5} - \sqrt{2}) }{ (\sqrt{5} + \sqrt{2})( \sqrt{5} - \sqrt{2}) }$
⇒$\frac{6( \sqrt{5} - \sqrt{2}) }{ \sqrt{5} ^{2} - \sqrt{2} ^{2} }$
⇒$\frac{6( \sqrt{5} - \sqrt{2}) }{5 - 2}$
⇒$\frac{6( \sqrt{5} - \sqrt{2}) }{3}$
⇒$2( \sqrt{5} - \sqrt{2})$
⇒$2 \sqrt{5} - 2 \sqrt{2}$