Question

Q8. On rationalising the denominator of we will get - (1 + sqrt(2))/(2 - sqrt(2))​

Answer 1

Answer:

Given

$\frac{1 + \sqrt{2} }{1 - \sqrt{2} } \\ = \frac{1 + \sqrt{2} }{1 - \sqrt{2} } \times \frac{1 + \sqrt{2} }{1 + \sqrt{2} } \\ = \frac{(1 + \sqrt{2} ) {}^{2} }{1 {}^{2} - ( \sqrt{2} ) {}^{2} } \\ = \frac{1 {}^{2} + 2 \times 1 \times \sqrt{2} + ( \sqrt{2} ) {}^{2} }{1 - 2} \\ = \frac{1 + 2 \sqrt{2} + 2}{ - 1} \\ = \frac{3 + 2 \sqrt{2} }{ - 1} \\ = - (3 + 2 \sqrt{2} )$