Question

rationalize the denominator of 5+root6/5-root6


give me the answer

Answer 1

(5+√6)/(5-√6)
= [(5+√6)(5+√6)]/[(5-√6)(5+√6)]
=[25+6+10√6]/[25-6]
=[31+10√6]/19

Answer 2

Answer:

$\frac{5+\sqrt{6}}{5-\sqrt{6}}=\frac{31}{19}+\frac{+10\sqrt{6}}{19}$

Step-by-step explanation:

Given expression,

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

We have to rationalize the denominator of the given expression.

Consider,

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

Multiply and divide by 5 + √6

we get,

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

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

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

$\implies\frac{25+6+10\sqrt{6}}{25-6}$

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

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

Therefore, $\frac{5+\sqrt{6}}{5-\sqrt{6}}=\frac{31}{19}+\frac{+10\sqrt{6}}{19}$