Which of the following is irrational?

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

Question

(D) number is irrational if and only if its decimal representation is non-terminating and non-recurring.$(A)$ $0.14$ is a terminating decimal,so it is

Vedclass · Accepted Answer

$0.4014001400014 \ldots$

Vedclass · Answer

(D) number is irrational if and only if its decimal representation is non-terminating and non-recurring.$(A)$ $0.14$ is a terminating decimal,so it is a rational number.$(B)$ $0.14 \overline{16}$ is a non-terminating and recurring decimal,so it is a rational number.$(C)$ $0. \overline{1416}$ is a non-terminating and recurring decimal,so it is a rational number.$(D)$ $0.4014001400014 \ldots$ is a non-terminating and non-recurring decimal,which is the definition of an irrational number.Hence,$(D)$ is the correct answer.

Similar Questions

State whether the following statement is true or false. Justify your answer.
$\frac{\sqrt{15}}{\sqrt{3}}$ is written in the form $\frac{p}{q},$ where $q \neq 0,$ so it is a rational number.

Represent $\sqrt{5.6}$ on the number line.

Represent $\sqrt{9.3}$ on the number line.

Show how $\sqrt{5}$ can be represented on the number line.

State whether the following statement is true or false:
$\sqrt{49}$ is an irrational number.

Vedclass Test Series

Exam Paper Generator

Online Exam Module