14 solutions available
Use Euclid’s Division Algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of...
Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
Use Euclid’s Division Lemma to show that the cube of any positive integer is either of the form 9m, 9m + 1 or 9m + 8.
Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = Product of the two numbers: (i) 26 and 91 (ii) 510 and 92 (iii)...
Find the LCM and HCF of the following integers by applying the prime factorization method: (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25
Prove that the following are irrational.
Prove that √5 is irrational.
Show that 3 + √5 is irrational.
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or...
Write down the decimal expansions of those rational numbers in question 1, which have terminating decimal expansions.
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational and of...
