Question

rationalise the denominator 5+√6/5-√6

Answer 1

hey friend,here's your answer in the attachment.
hope it helps.
#aditya

Answer 2

Answer:

$\frac{5+\sqrt{6}}{5-\sqrt{6}}$

= $\frac{31+10\sqrt{6}}{19}$

Explanation:

Given $\frac{5+\sqrt{6}}{5-\sqrt{6}}$

multiply numerator and denominator by $(5+\sqrt{6})$, we get

= $\frac{(5+\sqrt{6})(5+\sqrt{6})}{(5-\sqrt{6})(5+\sqrt{6})}$

= $\frac{(5+\sqrt{6})^{2}}{5^{2}-\left(\sqrt{6}\right)^{2}}$

_________________________

By the algebraic identities:

1) x²-y² = (x+y)(x-y)

2) (x+y)² = x²+2xy+y²

_________________________

= $\frac{(5^{2}+(\sqrt{6})^{2}+2\times5\times\sqrt{6}}{25-6}$

= $\frac{25+6+10\sqrt{6}}{19}$

= $\frac{31+10\sqrt{6}}{19}$

Therefore,

$\frac{5+\sqrt{6}}{5-\sqrt{6}}$

= $\frac{31+10\sqrt{6}}{19}$