Real Numbers

6 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 Find the HCF and the LCM of 306 and 657, and verify that HCF × LCM = product of the two numbers. medium 3 marks Relationship between HCF and LCM
• 2 Prove that √5 is an irrational number. medium 3 marks Proving irrationality by contradiction
• 3 Without performing long division, state whether 13/3125 has a terminating or a non-terminating repeating decimal expansion. Write the expansion if it terminates. easy 2 marks Condition for a terminating decimal expansion
• 4 Check whether 6^n can end with the digit 0 for any natural number n. medium 2 marks Fundamental Theorem of Arithmetic
• 5 Explain why 7 × 11 × 13 + 13 is a composite number. easy 2 marks Composite numbers and factorisation
• 6 Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they all toll together at 8:00 a.m., at what time will they next toll together? medium 3 marks Using the LCM for repeating events