Question

5-root 11 / 5 + root 11 , simplify by rationalizing the Denominator




Will it be 18-5 root 11/ 7?​

Answer 1

Step-by-step explanation:

$= \frac{5 - \sqrt{11} }{5 + \sqrt{11} } \\ = \frac{5 - \sqrt{11} }{5 + \sqrt{11} } . \frac{5 - \sqrt{11} }{5 - \sqrt{11} } \\ = \frac{5(5 - \sqrt{11} ) - \sqrt{11}(5 - \sqrt{11} ) }{5(5 - \sqrt{11} ) + \sqrt{11}(5 - \sqrt{11} )} \\ = \frac{25 - 5 \sqrt{11} - 5 \sqrt{11} + \sqrt{121} }{25 - \sqrt{121} } \\ = \frac{25 - 10 \sqrt{11} + 11}{25 - 11} \\ = \frac{36 - 10 \sqrt{11} }{14} \\ = \frac{18 - 5 \sqrt{11} }{7}$