Question

$\text{If}m=\frac{1}{3-2\sqrt{2}}\text{then,}{m}^2=$ _______.

• A. $34$
• B. $17-12\sqrt{2}$
• C. $24\sqrt{2}$
• D. $17+12\sqrt{2}$

Answer 1

The correct option is D

$17+12\sqrt{2}$

$m=\frac{1}{3-2\sqrt{2}}$

$m=\frac{1}{3-2\sqrt{2}}\times \frac{3+2\sqrt{2}}{3+2\sqrt{2}}$

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

$=\frac{3+2\sqrt{2}}{9-8}$

$=3+2\sqrt{2}$

$m^2=(3+2\sqrt{2}{)}^2$

$=(3{)}^2+2(3\left)\right(2\sqrt{2})+(2\sqrt{2}{)}^2$

$=9+12\sqrt{2}+8$

$=17+12\sqrt{2}$