Question

Which of the following is irrational number?

• A. $\frac{4}{5}$
• B. $\sqrt{81}$
• C. $\sqrt{7}$
• D. $\sqrt{\frac{4}{9}}$

Answer 1

The correct option is C $\sqrt{7}$

(i) $\sqrt{\frac{4}{9}}$
We know that,
$\sqrt{4}=2and\sqrt{9}=3\therefore \sqrt{\frac{4}{9}}=\frac{2}{3}$
$\frac{2}{3}$ is a rational number.
(Any number which can be expressed in the form $\frac{p}{q}$ [p, q are integers and $q\ne 0$] are known as rational numbers.)

(ii) $\frac{4}{5}$
$\frac{4}{5}$ is a rational number.
(Any number which can be expressed in the form $\frac{p}{q}$ [p, q are integers and $q\ne 0$] are known as rational numbers.)

(iii) $\sqrt{7}$
$\sqrt{7}$ is an irrational number as it cannot be expressed in the form $\frac{p}{q}$.

(Numbers which cannot be written in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0 are known as irrational numbers.)

(iv) $\sqrt{81}$
We know that,
$9^2=81\therefore \sqrt{81}=9=\frac{9}{1}$
$\frac{9}{1}$ is a rational number.
(Any number which can be expressed in the form $\frac{p}{q}$ [p, q are integers and $q\ne 0$] are known as rational numbers.)