Question

Find the value of $(1+\sqrt{2}{)}^2$.

• A. $3+2\sqrt{2}$
• B. $2+3\sqrt{2}$
• C. $3-2\sqrt{2}$
• D. $2-2\sqrt{2}$

Answer 1

The correct option is A

$3+2\sqrt{2}$

Using the formula $(a+b{)}^2=a^2+b^2+2ab$

$\Rightarrow (1+\sqrt{2}{)}^2=1^2+{\sqrt{2}}^2+2\sqrt{2}$

$=1+2+2\sqrt{2}$

$=3+2\sqrt{2}$