Irrational Numbers

Q.

The numbers which have a non-terminating and non-repeating decimal expansion and cannot be represented in the form of $\frac{p}{q}$ ( $q$ is not equal to '0') are known as___ numbers.

1. irrational

2. rational

3. real

4. integers

Q.

Which of the following fractions is a terminating decimal?

1. $\frac{1}{5}$

2. $\frac{1}{6}$

3. $\frac{1}{7}$

4. $\frac{1}{3}$

Q.

$2\sqrt{3}\times 3\sqrt{2}$ is a/an ___ number. (rational/irrational)

.

Q.

Which of the following fraction is terminating decimal?

1. 

2. 

3. 

4. 

Q.

Which of the following is an irrational number?

i) $2\sqrt{3}$

ii) $0.143\overline{32}$

iii) $5.\overline{46}$

iv) $\sqrt{5}$

1. Only iv)

2. ii) and iii)

3. i) and iv)

4. All of these

Q.

A circle has a radius of $7cm.$ What is the nature of the value of its circumference?

1. Integer

2. Rational

3. Whole number

4. Irrational

Q.

The value of the area of an equilateral triangle is irrational. What can you say about the sides of the triangle?

1. Can be either irrational or rational

2. Irrational always

3. Rational always

4. Integer always

Q.

Which of the following is an irrational number?

i) $2\sqrt{3}$

ii) $0.143\overline{32}$

iii) $5.\overline{46}$

iv) $\sqrt{5}$

1. Only iv

2. ii and iii

3. i and iv

4. Cannot be determined

Q.

Which of the following is always rational?

1. The hypotenuse of a right angled triangle having rational base and perpendicular

2. The area of a triangle​, given the value of the sides are irrational

3. The volume of a cube, given the value of the sides are rational

4. The area of rectangle in which the value of one of the sides is irrational

Q.

Which of the following is/are an irrational number?

1. $\pi$
   

2. $\sqrt{5}$
   

3. $\sqrt{7}$

4. $\frac{22}{7}$