Question

Rationalize the denominator of the following root 5 + root 2 by root 5 _ root 2​

Answer 1

Answer is given below

Answer 2

$\sf{ \large{\frac{\sqrt {5} + \sqrt{2} }{\sqrt{5 }- \sqrt{2} } }}$

$\implies \sf{ \large{\frac{\sqrt{5 }+ \sqrt{2} }{\sqrt{5 }- \sqrt{2} } } \times \frac{\sqrt{5} + \sqrt{2} }{\sqrt{5 }+ \sqrt{2} } }$

$\implies \sf{ \large{\frac{{(\sqrt{5} + \sqrt{2})}^{2} }{ {(\sqrt{5})}^{2} - {(\sqrt{2})}^{2} } }}$

$\implies \sf{ \large{\frac{{{(\sqrt{5})}^{2} + (\sqrt{2})}^{2} + 2(5)( \sqrt{2} ) }{ 5 - 2} }}$

$\implies \sf{ \large{\frac{{5 + 2} + 10\sqrt{2} }{ 3} }}$

$\implies \sf{ \large{\frac{{7} + 10\sqrt{2} }{ 3} }}$