Question

solve this by rationalise the number.

Answer 1

Hello Mate!

$x = \frac{1}{3 - \sqrt{8} } \\ \frac{1}{3 - \sqrt{8} } \times \frac{3 + \sqrt{8} }{3 + \sqrt{8} } \\ \frac{3 + \sqrt{8} }{9 - 8} = 3 + \sqrt{8} \\ {x}^{3} = {(3 + \sqrt{8} )}^{3} \\ = 27 + 8 \sqrt{8} + 3 \times {3}^{2} \times \sqrt{8} + 3 \times 3 \times { \sqrt{8} }^{2} \\ = 27 + 8 \sqrt{8} + 27 \sqrt{8} + 72 \\ = 99 + 35 \sqrt{8} \\ 2 {x}^{2} = 2 {(3 + \sqrt{8}) }^{2} \\ 2(9 + 8 + 6 \sqrt{8} ) = 34 + 12 \sqrt{8} \\ 7x = 7(3 + \sqrt{8} ) = 21 + 7 \sqrt{8} \\ 99 + 35 \sqrt{8} - 34 - 12 \sqrt{8} - 21 - 7 \sqrt{8} + 5 \\ = 49+ 16 \sqrt{8} \\ = 49 + 32 \sqrt{2}$

Hope it helps☺!