Question

3 + √5/ 3 - √5


........Rationalise .....

Answer 1

Answer in attachement

Answer 2

How to Rationalise

To rationalise any of the fractional number

Firstly you will find any of the irrational number at denominator

So , Firstly multiply the same number given in denominator to both Numerator & Denominator

Note :- You have to change the sign of number present at denominator then you have multiply with both Numerator & denominator ...

Now do like this

$\frac{3 + \sqrt{5} }{3 - \sqrt{5} } \\ \\ = \geqslant \frac{3 + \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \\ = \geqslant \frac{(3 + \sqrt{5} ) {}^{2} }{ {3}^{2} - { \sqrt{5} }^{2} } \\ \\ = \geqslant \frac{9 + 5 + 6 \sqrt{5} }{9- 5} \\ \\ = \geqslant \frac{14 + 6 \sqrt{5} }{4} \\ \\ = \geqslant \frac{2(7 + 3 \sqrt{5}) }{4} \\ \\ = \geqslant \frac{7 + 3 \sqrt{5} }{2}$