Real Numbers : Assessment for classes IX and X

Prime Maths

25 Question MCQ Chapter on Real Numbers for CBSE, ICSE, Madhyamik and other State Boards Class IX & X

👨‍🏫 Author: Singh

📞 WA: +91-9038126497

Prime Maths

Real Numbers Quiz

Test your understanding of rational, irrational numbers and their properties. The study of Real Numbers in Classes IX and X establishes the foundation for all higher-level mathematics.Real Numbe: The set including all Rational and Irrational numbers. Rational Numbers: Numbers expressible as p/q, q is non-zero . Their decimal expansions are either terminating or non-terminating recurring.Irrational Numbers: Numbers that cannot be written as fractions. Their decimal expansions are non-terminating non-recurring.Number Line: Every point on a number line represents a unique real number.

0

Done

25

Left

0%

Score

📝 Instructions

• This quiz contains 25 multiple choice questions on Real Numbers.
• Select only one correct answer per question.
• Use the navigator to jump between questions.
• Submit when you are finished to see results.

Question Navigator

Progress 0%

Question 1

Which of the following is an irrational number?

A\(\sqrt{25}\) B\(\sqrt{2} + \sqrt{3}\) C\(\frac{3}{7}\) D\(0.\overline{3}\)

Question 2

The decimal expansion of \(\frac{13}{625}\) will terminate after how many decimal places?

A2 B3 C4 D5

Question 3

Which of the following has a terminating decimal expansion?

A\(\frac{77}{210}\) B\(\frac{23}{30}\) C\(\frac{125}{441}\) D\(\frac{129}{2^2 \times 5^7}\)

Question 4

The simplified value of \(\sqrt{12} + \sqrt{27} - \sqrt{75}\) is:

A\(\sqrt{3}\) B\(2\sqrt{3}\) C\(3\sqrt{3}\) D\(0\)

Question 5

If \(p\) and \(q\) are co-prime numbers, then \(p^2\) and \(q^2\) are:

ACo-prime BNot co-prime CEven numbers DOdd numbers

Question 6

A rational number between \(\sqrt{2}\) and \(\sqrt{3}\) is:

A\(\frac{\sqrt{2} + \sqrt{3}}{2}\) B\(\frac{\sqrt{2} \times \sqrt{3}}{2}\) C\(1.5\) D\(1.8\)

Question 7

The value of \(1.\overline{36} + 0.\overline{9}\) is:

A\(2.\overline{27}\) B\(2.\overline{26}\) C\(2.\overline{3}\) D\(2.3\)

Question 8

Which of the following is not an irrational number?

A\(\sqrt{8} \times \sqrt{2}\) B\(\sqrt{18} \div \sqrt{2}\) C\(\sqrt{5} + \sqrt{10}\) D\(\sqrt{7} \times \sqrt{28}\)

Question 9

If \(n\) is a natural number, then \(\sqrt{n}\) is:

AAlways rational BAlways irrational CRational if \(n\) is a perfect square DIrrational if \(n\) is a perfect square

Question 10

The product of a non-zero rational and an irrational number is:

AAlways rational BAlways irrational CCan be rational or irrational DAlways an integer

Question 11

Which of the following rational numbers have terminating decimal representation?

A\(\frac{16}{125}\) B\(\frac{27}{250}\) C\(\frac{343}{2^3 \times 5^3}\) DAll of these

Question 12

The ascending order of \(\sqrt[3]{2}, \sqrt{3}, \sqrt[6]{5}\) is:

A\(\sqrt[3]{2} < \sqrt[6]{5} < \sqrt{3}\) B\(\sqrt[6]{5} < \sqrt[3]{2} < \sqrt{3}\) C\(\sqrt[6]{5} < \sqrt{3} < \sqrt[3]{2}\) D\(\sqrt{3} < \sqrt[3]{2} < \sqrt[6]{5}\)

Question 13

The decimal expansion of the rational number \(\frac{14587}{1250}\) will terminate after:

AOne decimal place BTwo decimal places CThree decimal places DFour decimal places

Question 14

After rationalizing the denominator of \(\frac{7}{3\sqrt{3} - 2\sqrt{2}}\), we get:

A\(3\sqrt{3} + 2\sqrt{2}\) B\(3\sqrt{3} - 2\sqrt{2}\) C\(7(3\sqrt{3} + 2\sqrt{2})\) D\(7(3\sqrt{3} - 2\sqrt{2})\)

Question 15

An irrational number between \(\frac{1}{7}\) and \(\frac{2}{7}\) is:

A\(\frac{1}{2}\left(\frac{1}{7} + \frac{2}{7}\right)\) B\(\sqrt{\frac{1}{7} \times \frac{2}{7}}\) C\(\frac{1}{\sqrt{14}}\) D\(\sqrt{0.14}\)

Question 16

If \(x = 2 + \sqrt{3}\), then \(x + \frac{1}{x}\) equals:

A\(4\) B\(2\sqrt{3}\) C\(-4\) D\(-2\sqrt{3}\)

Question 17

Which of the following is a rational number?

A\(\pi\) B\(\sqrt{2}\) C\(0.\overline{101}\) D\(\sqrt{5} + 1\)

Question 18

The simplest rationalizing factor of \(\sqrt[3]{54}\) is:

A\(\sqrt[3]{2}\) B\(\sqrt[3]{3}\) C\(\sqrt[3]{4}\) D\(\sqrt[3]{9}\)

Question 19

If \(\frac{p}{q}\) is a rational number with terminating decimal expansion, where \(p\) and \(q\) are co-prime, then \(q\) must be of the form:

A\(2^m \times 3^n\) B\(2^m \times 5^n\) C\(3^m \times 5^n\) D\(2^m \times 3^n \times 5^k\)

Question 20

The sum of two irrational numbers is:

AAlways irrational BAlways rational CCan be rational or irrational DAlways an integer

Question 21

The value of \(\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \cdots + \frac{1}{\sqrt{99} + \sqrt{100}}\) is:

A\(1\) B\(9\) C\(10\) D\(99\)

Question 22

If \(a\) and \(b\) are rational numbers and \(\frac{3 + 2\sqrt{3}}{3 - 2\sqrt{3}} = a + b\sqrt{3}\), then \(a + b =\)

A\(11\) B\(-11\) C\(13\) D\(-13\)

Question 23

Which of the following is not true?

AEvery integer is a rational number BEvery whole number is a natural number CEvery irrational number is a real number DEvery rational number is a real number

Question 24

The product \(\sqrt[3]{2} \times \sqrt[4]{2} \times \sqrt[12]{32}\) equals:

A\(\sqrt{2}\) B\(2\) C\(\sqrt[12]{2}\) D\(\sqrt[12]{32}\)

Question 25

The value of \(0.\overline{6} + 0.\overline{7} + 0.\overline{4}\) is:

A\(2\) B\(\frac{17}{9}\) C\(\frac{53}{22}\) D\(\frac{59}{22}\)

Prime Maths - Excellence in Mathematical Education

© 2026 Prime Maths | Created by Vinod Singh