Worksheet for chapter: Real Numbers is presented below. The worksheets are provided for practice and self evaluation of students of class 10. Solutions are provided at the end of the page.
(1) Use Euclid’s division algorithm to find the HCF of:
(i) 4256 and 56 (ii) 8555 and 145
(2) Show that any positive odd integer is of the form 8q + 1, or 8q + 3 or 8q + 5, where q is some integer.
(3) Find the LCM and HCF of 210 and 33.
(4)Given that HCF (130, 510) = 10, find LCM(130, 510).
(5) Explain why 6 × 5 × 12 + 12 and 6 × 5 × 4 × 3 + 5 are composite numbers.
(6) Prove that the following are irrationals:
(i) 3 + √2 (ii) 5√2
(7)Decide whether following decimal expansions are rational or not. If they are rational, and of the form p/q , what can you say about the prime factors of q?
(i) 1.231646 (ii) 2.14135672…
(8) Without long division, state whether the following rational numbers will have a terminating decimal expansion or non – terminating repeating decimal expansion:
(9) A teacher has to manage 414 students to perform in a function in a group of 42 students. What is the maximum number of group in which they can perform?
(10) Check whether 8n can end with the digit 0 for any natural number n.
Helping Topics
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