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Class 10th Mathematics Chapter 1 Real Numbers – Important Questions

Important questions with answers for Class 10th Mathematics Chapter 1 Real Numbers, based on the NCERT CBSE syllabus.

Topics covered in Real Numbers

Frequently asked questions

Where can I find important questions for Class 10th Mathematics Chapter 1 Real Numbers?

This page lists important questions with answers for Real Numbers. Topics covered: Euclid's division lemma, HCF and LCM, Fundamental theorem of arithmetic, Irrational numbers.

Are Real Numbers important questions free?

Yes, Notebook gives free NCERT CBSE important questions for Class 10 Mathematics.

How to prepare Real Numbers for Class 10 Mathematics exams?

Read the Real Numbers notes first, revise the key topics (Euclid's division lemma, HCF and LCM, Fundamental theorem of arithmetic, Irrational numbers), then practise the important questions and previous year questions (PYQ) for this chapter.

Where can I find Class 10th Mathematics Chapter 1 Real Numbers important questions for quick revision?

You are on the right page: this important questions page for Real Numbers covers Class 10 Mathematics for the CBSE exam 2026-27. Use the tabs on this chapter for notes, important questions and PYQ.

Is Class 10th Mathematics Chapter 1 Real Numbers important for the CBSE exam 2026-27?

Real Numbers is part of the Class 10 Mathematics NCERT CBSE syllabus. Notebook gives notes, important questions and PYQs for it, free.

Also see: Class 10th Mathematics Chapter 1 Real Numbers Notes · Class 10th Mathematics Chapter 1 Real Numbers PYQ

Real Numbers

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1 Mark
State the Fundamental Theorem of Arithmetic.
Ans: Every composite number can be expressed as a product of primes in a unique way, regardless of the order of factors.
2 Marks
Find the HCF of 96 and 404 using Euclid's Division Algorithm.
Ans: 404 = 96×4 + 20; 96 = 20×4 + 16; 20 = 16×1 + 4; 16 = 4×4 + 0. HCF = 4.
3 Marks
Prove that √2 is irrational.
Ans: Assume √2 = p/q (lowest terms). Then 2q² = p², so p² is even → p is even → p = 2m. Then 2q² = 4m² → q² = 2m² → q is even. But p and q both even contradicts lowest terms. Hence √2 is irrational.
3 Marks
Check whether 6ⁿ can end with the digit 0 for any natural number n.
Ans: For a number to end in 0 it must be divisible by 10 = 2×5. Prime factorisation of 6ⁿ = 2ⁿ × 3ⁿ. Since 5 is not a factor, 6ⁿ can never end in 0.
Other chapters in Mathematics · Class 10 View all Mathematics chapters →
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