Question

Which of the given options is an irrational number?

• A. 3.141592
• B. $\frac{5}{\sqrt{625}}$
• C. $\sqrt{1681}$
• D. $\sqrt{0.9}$

Answer 1

The correct option is D $\sqrt{0.9}$

Irrational numbers are those that cannot be written in the form of p/q, where p and q are integers, and q ≠ 0.

Option(a) - 3.141592 is a rational number.
Option(b) - $\frac{5}{\surd 625}$ = $\frac{5}{25}$ = $\frac{1}{5}$ = $\frac{p}{q}$, hence a rational number.
Option(c) - $\sqrt{1681}$ = 41 = $\frac{41}{1}$ = $\frac{p}{q}$, hence a rational number.
Option(d) - $\sqrt{0.9}$ = $\sqrt{\frac{9}{10}}$ = $\frac{3}{\sqrt{10}}$, we know that $\sqrt{10}$ is an irrational number which makes the whole term an irrational number. Hence, $\sqrt{0.9}$ is an irrational number