Question

Rationalize the denominator of root 7-2/root 7+2

Answer 1

$\implies\sf \red{ \frac{ \sqrt{7} - 2 }{ \sqrt{7} + 2} } \\ \implies \sf{ \frac{ \sqrt{7 } - 2}{ \sqrt{7} + 2} \times \frac{ \sqrt{7} - 2}{ \sqrt{7} - 2 } } \\ \implies \sf{ \frac{ \sqrt{( {7})^{2} } - 2 \times \sqrt{7} \times 2 + {(2)}^{2} }{7 - 4} } \\ \implies \sf{ \frac{7 - 4 \sqrt{7} + 4 }{3} } \\ \implies \sf{ \frac{11 - 4 \sqrt{7} }{3} } \\ \therefore \sf \red{ \frac{ 7\sqrt{7} }{3} }$