Representing Irrational Number on Number Line

Q.

Distance between $\sqrt{2}$ & -$\sqrt{2}$ on the number line approximately is _____________.

1. 1.4 units

2. 4.2 units

3. 2.8 units

4. 8.4 units

Q.

Which of the following is not logically equivalent to the proposition: “A real number is either rational or irrational”?

1. If a number is neither rational nor irrational then it is not real

2. If a number is not a rational or not an irrational, then it is not real

3. If a number is not real, then it is neither rational nor irrational

4. If a number is real, then it is rational or irrational

Q. Which of the following are irrational numbers?
I. $\frac{22}{7}$
II. $\frac{1}{3}$
III. $3.36$
IV. $\sqrt{6}$

1. III and IV
   
2. Only IV
   
3. Only III
   
4. II and III
   

Q.

If $n$is a natural number then root $n$is ?

Q. Which of the following is irrational?

1. $\sqrt{81}$
2. $\sqrt{\frac{4}{9}}$
3. $\sqrt{7}$
4. $\frac{4}{5}$

Q. Classify the following numbers as rational or irrational
(i) $\sqrt{23}$
(ii) $\sqrt{225}$

Q. If $1176=2^a\times 3^b\times 7^c$, what is the value of b?

1. 1
2. 2
3. 3
4. 4

Q.

Examine whether the following number is rational or irrational:

$-\sqrt{81}$

Q. Represent the following irrational number on the number line.
$\sqrt{6.5}$
$\left[4\right]$

Q. $\sqrt{2}$ is not an irrational number.

1. True
2. False

Q. $\sqrt{2}$ lies between on the number line.

1. 0 and 1
2. 1 and 2
3. 2 and 3

Q.

An irrational number is marked on the number line (C) as shown in fig. Then the value of C is ___.

1. $\sqrt{7}$

2. $\sqrt{5}$

3. $\sqrt{2}$

4. $\sqrt{3}$

Q.

Where would the number $\sqrt{2}$ lie on the number line?

1. between $0$ and $1$

2. between $1$ and $2$

3. between $2$ and $3$

4. between $-1$ and $-2$

Q.

Classify the following numbers as rational or irrational :

$\sqrt{23}$

Q. Classify the following numbers as rational or irrational
(i) $\sqrt{23}$
(ii) $\sqrt{225}$
(iii) 0.3796

[ 3 marks ]

Q. The square root of 16 .

1. is rational
2. is irrational
3. doesn't exist

Q. Irrational numbers can be located on the number line using Pythagoras' theorem.

1. False
2. True

Q.

An irrational number is marked on the number line (D) as shown in the figure below. Then the value of D is ________.

1. $\sqrt{5}$

2. $\sqrt{7}$

3. $\sqrt{3}$

4. $\sqrt{10}$

Q. Which of the following are rational numbers?

1. 1
2. 2.33
3. π
4. \N
5. 4.256258...
6. -10
7. 100
8. 1.41432...