Question

The multiplicative inverse of $-1+\sqrt{2}$ is

• A. $-1-\sqrt{2}$
• B. $1-\sqrt{2}$
• C. $1+\sqrt{2}$
• D. $\sqrt{2}$
• E. $2-\sqrt{2}$

Answer 1

Answer: (C)

$1+\sqrt{2}$

Multiplicative inverse of $\sqrt{2}-1$ is $\frac{1}{\sqrt{2}-1}$
Now multiply and divide with $\sqrt{2}+1$
We get $\frac{\sqrt{2}+1}{(\sqrt{2}+1)(\sqrt{2}-1)}$

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

$=\sqrt{2}+1$