Which of the following is irrational?

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(C) To determine which number is irrational,we simplify each option:$(a)$ $\sqrt{\frac{4}{9}} = \frac{2}{3}$,which is a rational number because it can

Vedclass · Accepted Answer

$\sqrt{7}$

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(C) To determine which number is irrational,we simplify each option:$(a)$ $\sqrt{\frac{4}{9}} = \frac{2}{3}$,which is a rational number because it can be expressed in the form $\frac{p}{q}$ where $p, q$ are integers and $q 
eq 0$.$(b)$ $\frac{\sqrt{12}}{\sqrt{3}} = \sqrt{\frac{12}{3}} = \sqrt{4} = 2$,which is a rational number.$(c)$ $\sqrt{7}$ cannot be simplified into a fraction of integers. Since $7$ is not a perfect square,$\sqrt{7}$ is an irrational number.$(d)$ $\sqrt{81} = 9$,which is a rational number.Therefore,$\sqrt{7}$ is the irrational number. Hence,$(C)$ is the correct answer.

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