Which of the following is irrational?

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$\sqrt{7}$

Vedclass · Answer

(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.

Similar Questions

The value of $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is equal to

For each question,select the proper option from four options given,to make the statement true: $.............$ is a rational number between $7$ and $8$.

Multiply $5 \sqrt{3}$ and $4 \sqrt{12}$.

If $\sqrt{2} = 1.4142$,then evaluate $\sqrt{5} \div \sqrt{10}$ correct to four decimal places.

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{1}{\sqrt{3}+\sqrt{2}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module