Real Numbers

What you'll learn

The number family tree, the HCF×LCM rule, and how to tell rational from irrational — the Class 10 essentials.

This chapter has

Real Numbers — solved practice questions

6 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   What is the HCF of 12 and 18?

   • A2
   • B3
   • C6
   • D9
   Show answer & solution

   Correct answer: (C) 6

   12 = 2²×3, 18 = 2×3². Common factors: 2×3 = 6. So HCF = 6.

2. Q2easy

   What is the LCM of 4 and 6?

   • A10
   • B12
   • C18
   • D24
   Show answer & solution

   Correct answer: (B) 12

   Multiples of 4: 4, 8, 12… Multiples of 6: 6, 12… The smallest common one is 12.

3. Q3medium

   For any two positive integers, HCF × LCM equals:

   • Athe sum of the numbers
   • Bthe product of the numbers
   • Cthe difference
   • Dthe quotient
   Show answer & solution

   Correct answer: (B) the product of the numbers

   A key property: HCF(a,b) × LCM(a,b) = a × b (the product of the two numbers).

4. Q4medium

   Which of the following is an irrational number?

   • A0.5
   • B2/3
   • C√2
   • D1.75
   Show answer & solution

   Correct answer: (C) √2

   √2 cannot be written as p/q, so it is irrational. 0.5, 2/3 and 1.75 are all rational.

5. Q5medium

   The decimal expansion of a rational number is either terminating or:

   • Anon-terminating non-repeating
   • Bnon-terminating repeating
   • Calways terminating
   • Dundefined
   Show answer & solution

   Correct answer: (B) non-terminating repeating

   Every rational number has a decimal expansion that is terminating or non-terminating recurring (repeating).

6. Q6easy

   If the HCF of two numbers is 1, the numbers are called:

   • Aequal
   • Bco-prime
   • Ccomposite
   • Deven
   Show answer & solution

   Correct answer: (B) co-prime

   Two numbers with HCF = 1 share no common factor other than 1 — they are called co-prime.

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