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(i) 1057

(ii) 23453

(iii) 7928

(iv) 222222

(v) 64000

(vi) 89722

(vii) 222000

(viii) 505050

Answer :

For checking a number to be perfect square we need to see the unit's digit or the number of digits repeating from the end of the number given.If the unit's digit is perfect square then it may be a perfect square.Also if the number of digits repeating are odd in number then it won't be a perfect square.So here we have:

(i) It is not a perfect square number because 1057 ends with 7 at unit place.

(ii) It is not a perfect square number because 23453 ends with 3 at unit place.

(iii) It is not a perfect square number because 7928 ends with 8 at unit place.

(iv) It is not a perfect square number because 222222 ends with 2 at unit place.

(v) It is not a perfect square number because 64000 ends with odd number of zeros i.e, 3.

(vi) It is not a perfect square number because 89722 ends with 2 at unit place.

(vii) It is not a perfect square number because 22000 ends with 3 zeros.

(viii) It is not a perfect square number because 505050 ends with 1 zero.

- 1.What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 20387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555
- 3.The squares of which of the following would be odd numbers? (i) 431 (ii) 2826 (iii) 7779 (iv) 82004
- 4.Observe the following pattern and find the missing digits. \(11^2\) = 121 \(101^2\) = 10201 \(1001^2\) = 1002001 \(100001^2\) = 1…2…1 \(10000001^2\) = ………
- 5.Observe the following pattern and supply the missing numbers. \(11^2\) = 121 \(101^2\) = 10201 \(10101^2\) = 102030201 \(1010101^2\) = ………. \(……….^2\) = 10203040504030201
- 6.Using the given pattern, find the missing numbers. \(1^2 + 2^2 + 2^2 = 3^2\) \(2^2 + 3^2 + 6^2 = 7^2\) \(3^2 + 4^2 + 12^2 = 13^2\) \(4^2 + 5^2 + ….^2 = 21^2\) \(5^2 + ….^2 + 30^2 = 31^2\) \(6^2 + 7^2 + …..^2 = ……2\)
- 7.Without adding, find the sum. (i) 1 + 3 + 5 + 7 + 9 (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
- 8. (i) Express 49 as the sum of 7 odd numbers. (ii) Express 121 as the sum of 11 odd numbers.
- 9.How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100.

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