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Show that 3√2 is irrational.
Show that 5 – √3 is irrational.
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 of the form 9m,9m+1or9m+8
Consider the numbers , where n is a natural number. Check whether there is any value of n for which ends with the digit zero.
5. Check whether 6^n can end with the digit 0 for any natural number n.
Find the LCM and HCF of the following integers by applying the prime factorisation method of 12,15 and 21
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 columns. What is the maximum number of columns in which they can march?
Sol:- Maximum number of columns = HCF(32, 616) By Euclid's division method, 616 = 32 × 19 + 8 32 = 8 × 4 + 0 ∴ HCF(32, 616) = 8 Maximum number of columns = 8
Sol:-
Maximum number of columns = HCF(32, 616)
By Euclid’s division method,
616 = 32 × 19 + 8
32 = 8 × 4 + 0
∴ HCF(32, 616) = 8
Maximum number of columns = 8
See lessExplain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers
Given that HCF (306, 657) = 9, find LCM (306, 657)
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