Identification of Rational and Irrational Numbers

Q. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.

Q. Look at several examples of rational numbers in the form $\frac{p}{q}(q\ne 0)$, where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representaions (expansions). Can you guess what property $q$ must satisfy?

Q. Insert a rational and an irrational number between $2$ and $3$.

Q.

Which of the following is an irrational number?

1. $2\sqrt{3}$
2. $0.143\overline{32}$
3. $5.\overline{46}$
4. $\sqrt{5}$

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. Only iii

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. ii and iii
2. i and iv
3. Only iv
4. All of the above

Q.

The number ${(1+\sqrt{3})}^2$ is a/an ____________.

1. natural number

2. rational number

3. irrational number

4. integer

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 the above

Q.

Which of the following is an irrational number?

1. 14.287628762876.....

2. 15.2323232323......

3. 5.2731687143725186.....

4. 1.33333333...

Q. Which of the following numbers is particularly an irrational number between 2 and 3?

1. 2.579
2. 2.345345345...
3. 2.101001000..
4. 2.05131313...

Q. Which of the following is/are an irrational number?

1. $\pi$

2. $\sqrt{5}$

3. $\sqrt{7}$

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