# Mathematics Questions and Answers – Irrational Numbers

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Irrational Numbers”.

1. Irrational numbers are denoted by _______
a) N
b) Z
c) Q
d) S

Explanation: As per the conventional notation, irrational numbers are denoted by ‘S’.
N, Z and Q are used for Natural numbers, Integers and Rational numbers respectively.

2. $$\frac{1 + \sqrt{3}}{2}$$ is ____________
a) rational number
b) irrational number
c) natural number
d) integer

Explanation: According to definition, a number is said to be irrational if it can’t be represented in the form of p/q, where p and q are integers and q ≠ 0.
Here, $$\sqrt{3}$$ ≈ 1.73 which is not an integer. So as per the definition, the given number is irrational number.

3. Real numbers are denoted by which letter?
a) R
b) W
c) Q
d) N

Explanation: As per the conventional notation, irrational numbers are denoted by ‘R’.
W, Q and N are used for Whole numbers, Rational numbers and Natural numbers respectively.
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4. All irrational numbers are real numbers.
a) True
b) False

Explanation: Real numbers comprise rational numbers and irrational numbers.
{Real numbers} = {Rational numbers} + {Irrational numbers}
Hence we can say that all irrational numbers are real numbers.

5. How many real numbers are there between 3 and 8 (Including 3 and 8)?
a) Six
b) Four
c) Infinite
d) Five

Explanation: There are infinite numbers between 3 and 8 like 3.45, 5.56, 5.95, 6, 7.41…. and so on. All these numbers are real according to the definition of real numbers
{Real numbers} = {Rational numbers} + {Irrational numbers}
Hence we can say that there are infinite real numbers between any two integers.

6. Which of the following is not irrational number?
a) $$\frac{\sqrt{9}}{2}$$
b) π
c) $$\frac{\sqrt{3}}{2}$$
d) $$\frac{\sqrt{11}}{2}$$

Explanation: $$\frac{\sqrt{9}}{2} = \frac{3}{2}$$ where 3 and 2 are integers. So $$\frac{3}{2}$$ is rational number by definition.
π ≈ 3.14, $$\sqrt{3}$$ ≈ 1.73 $$\sqrt{11}$$ ≈ 3.31
As we can see that none of the above three numbers is integer so they are not rational number by definition. (Rational number = p/q where p and q are integers and q ≠ 0).

7. Every point on the number line represents a unique real number.
a) True
b) False

Explanation: According to definition, Real numbers comprise rational and irrational numbers. So we can say that every point on number line represents a unique real number and vice versa.

8. Which of the following option is correct according to the below statements?
i) Every rational number is real number.
ii) Every real number is rational number.
a) Both statements are correct
b) Statement (i) is correct and statement (ii) is incorrect
c) Statement (i) is incorrect and statement (ii) is correct
d) Both statements are incorrect

Explanation: According to definition, {Real numbers} = {Rational numbers} + {Irrational numbers}
So every rational number is real number.
$$\sqrt{3}$$ is not rational number as it is not integer ($$\sqrt{3}$$ ≈ 1.73) but it is real number. Hence it is not necessary that every real number is rational number.

Sanfoundry Global Education & Learning Series – Mathematics – Class 9. 