Question

1/√(31+8√5) rationalize the denominator​

Answer 1

$\frac{1}{ \sqrt{31 + 8 \sqrt{5} } }$

$= \frac{1}{ \sqrt{31 + 8 \sqrt{5} } } \times \frac{ \sqrt{31 - 8 \sqrt{5} } }{ \sqrt{31 - 8 \sqrt{5} } }$

Using the identity,

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

$= \frac{ \sqrt{31 - 8 \sqrt{5} } }{ \sqrt{ {(31)}^{2} - {(8 \sqrt{5} )}^{2} } }$

$= \frac{ \sqrt{ 31 - 8 \sqrt{5} } }{ \sqrt{961 - 320} }$

$= \frac{ \sqrt{31 - 8 \sqrt{5} } }{ \sqrt{641} }$