Question

Which of the following is not irrational ?

• A. $$\frac{\sqrt2 +1}{\sqrt2-1}-2\sqrt{2}$$
• B. $\pi$
• C. $\sqrt{24}$
• D. $\frac{1}{\sqrt5}$

Answer 1

Answer:

$$\frac{\sqrt2 +1}{\sqrt2-1}-2\sqrt{2}$$

$\frac{\sqrt{2}+1}{\sqrt2-1}-2\sqrt2$

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

$=\frac{\sqrt{2}+1-4+2\sqrt2}{\sqrt2-1}$

$=\frac{3\sqrt2-3}{\sqrt2-1}$

$=\frac{3(\sqrt2-1)}{\sqrt2-1}$

$=3$