Question

Compute 1/(√2 + 1) correct to two decimal places.

• A. 0.71
• B. 0.41
• C. 0.58
• D. 0.50

Answer 1

Answer:

B. 0.41

$$mutiply with conjugate of $\sqrt2+1$

$\frac1{\sqrt2+1}=\frac{\sqrt2-1}{(\sqrt2+1)(\sqrt2-1)}$

$=\frac{\sqrt2-1}{(\sqrt2)^2-1^2}$

$=\frac{\sqrt2-1}{2-1}$

$=\sqrt2-1$

$=1.41-1$

$=0.41$