Question

find 1/root 9-root 8 your options are 1:1/2(3-2root2) 2:1/3+2root2 3:3-2root2 4:3+2root2

Answer 1

Answer:

I think it will be option 1

Answer 2

Option (4) 3+2√2 is correct.

$\frac{1}{ \sqrt{9} - \sqrt{8} } = \frac{1}{3 -2 \sqrt{2} } \\ \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ = \frac{3 + 2 \sqrt{2} }{(3)^{2} - (2 \sqrt{2} ) ^{2} } \\ = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ = \frac{3 + 2 \sqrt{2} }{1} \\ = 3 + 2 \sqrt{2}$

Remember:

a²-b²=(a+b)(a-b)