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) $\sqrt{81}$

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Solution

The answer is C.
$∵ \sqrt{\frac{4}{9}} = \frac{2}{3}$ (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.

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Similar questions

Q. 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}}

\sqrt{\frac{12}{3}}

\sqrt{7}

\sqrt{81}

Give as many examples there can be of irrational numbers and can you plz give me the definition of irrational no. As we were taught that irrational no. are the no. or fractions that r not terminating and non repeating

Q. Find whether the following statement are true or false.
(i) Every real number is either rational or irrational.
(ii)

π

is an irrational number.
(iii) Irrational numbers cannot be represented by points on the number line.

Q. If irrational number cannot be expressed in the form p/q where p and q are integers, and q is not = 0, then why pi is irrational though it is represented in the form p/q

If 1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form, then p + q is

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Irrational Numbers

Standard IX Mathematics

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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) √49 B) √123 C) √7 D) √81

The answer is C. ∵√49=23 (rational) √12√3=2√3√3=2 (rational) √81=9 (rational) But √7 is an irrational number. Hence, √7 is the irrational number among the given options.

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) $\sqrt{81}$

The answer is C.
$∵ \sqrt{\frac{4}{9}} = \frac{2}{3}$ (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.