Question

Select all irrational numbers.

Answer 1

Answer:

OPTION A

OPTION B

OPTION C

Step-by-step explanation:

Irrational numbers are the subset of real numbers. Their decimal representation neither form a pattern nor terminate.

OPTION A: $\sqrt{\frac{1}{2}}$

This is equal to $\frac{1}{\sqrt{2}}$.

$\sqrt{2} = 1.414...$ is non-terminating. So, it is an irrational number. Hence, the reciprocal of an irrational number would also be irrational. So, OPTION A is irrational.

OPTION B: $\sqrt{\frac{1}{8}}$

This is equal to $\frac{1}{2\sqrt{2}}$. Using the same logic as Option A, we regard OPTION B to be irrational as well.

OPTION C: $\sqrt{\frac{1}{10}}$

This is equal to $\frac{1}{\sqrt{5}\sqrt{2}}$.

Both $\sqrt{5}$ and $\sqrt{2}$ are irrational. So, the product and the reciprocal of the product is irrational as well. So, OPTION C is an irrational number.

OPTION D: $\sqrt{\frac{1}{16}}$

16 is a perfect square and is a rational number. $\frac{1}{\sqrt{16}}$ = $\frac{1}{4}$. This is equal to 0.25, a terminating decimal. So, OPTION D is a rational number.

OPTION E: $\sqrt{\frac{1}{4}}$

4 is a perfect square as well. $\frac{1}{\sqrt{4}} = \frac{1}{2} = 0.5$, a terminating decimal. So, OPTION E is a rational number.