Question

3 minus root 2 divided 3 plus root 2

Answer 1

Answer:

$\frac{3 - \sqrt{2} }{3 + \sqrt{2} } \\ = \frac{3 - \sqrt{2} }{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } \\ = \frac{ {(3 - \sqrt{2} )}^{2} }{ {3}^{2} - { \sqrt{2} }^{2} } \\ = 9 + 2 - 6\sqrt{2} \div 9 - 2 \\ = \frac{11 - 6 \sqrt{2} }{7}$

concept used , rationalising the denominator

and , identity

(a - b) ² = a² + b² -2ab