Question

Question 6
Which of the following is irrational?
Thinking process
An irrational number cannot be expressed as a fraction. It cannot be represented as a terminating or repeating decimal.

A) $\sqrt{\frac{4}{9}}$
B) $\sqrt{\frac{12}{3}}$
C) $\sqrt{7}$
D) $\sqrt{81}$

Answer 1

The answer is C.
$\because \sqrt{\frac{4}{9}}=\frac{2}{3}$ (rational)
$\frac{\sqrt{12}}{\sqrt{3}}=\frac{2\sqrt{3}}{\sqrt{3}}=2$ (rational)
$\sqrt{81}=9$ (rational)
But $\sqrt{7}$ is an irrational number.
Hence, $\sqrt{7}$ is the irrational number among the given options.