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Squares and Square Roots
Find whether each of the following numbers is a perfect square or not?
(i) 121 (ii) 55 (iii) 81
(iv) 49 (v) 69
(i) 121
∵ 121 - 1 = 120 85-13 = 72
120 - 3 = 117 72 - 15 = 57
117 - 5 = 112 54 - 17 = 40
112 - 7 = 105 40 - 19 = 21
105 - 9 = 96 21 - 21 = 0
96 - 11 = 85
i.e. 121 = 1+3+5+7+9+11+13+15+17+19+21. Thus , 121 is a perfact square.
(ii) 55
∵ 55 - 1 = 54 30 - 11 = 19
54 - 3 = 51 19 - 13 = 6
51 - 5 = 46 6 - 15 = -9
46 - 7 = 39
39 - 9 = 30
Since, 55 cannot be expressed as the sum of successive old numbers starting from 1.
∴ 55 is not a perfact square.
(iii) 81
Since, 81 - 1 = 80 56 - 11 = 45
80 - 3 = 77 45 - 13 = 32
77 - 5 = 72 32 - 15 = 17
72 - 7 = 65 17 - 17 = 0
65 - 9 =56
∴ 81 = 1+3+5+7+9+11+13+15+17
Thus, 81 is a perfact square.
(iv) 49
Since, 49 - 1 = 48
48 - 3 = 45
45 - 5 = 40
40 - 7 = 33
33 - 9 = 24
24 - 11 = 13
13 - 13 = 0
∴ 49 = 1+3+5+7+9+11+13
Thus, 69 is not a perfact square.
(v) 69
Since, 69 - 1 = 68 44 - 11 = 33
68 - 3 = 65 33 - 13 = 20
65 - 5 = 60 20 - 15 = 5
60 - 7 = 53 5 - 17 = 12
53 - 9 = 44
∴ 69 cannot be expressed as the sum of consecutive odd num numbers starting fron 1. Thus, 69 is not a perfect square.
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1. Can we say whether the following numbers are perfect squares? How do we know?
(i) 1057 (ii) 23453 (iii) 7928
(iv) 222222 (v) 1069 (vi) 2061
Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.
Write five numbers which you cannot decide just by looking at their unit’s digit (or one’s place) whether they are square numbers or not.
Which of 1232, 772 822, 1612, 1092 would end with digit 1?
Which of the following numbers would have digit 6 at unit place.
(i) 192 (ii) 242 (iii) 262
(iv) 362 (v) 342
What will be the “one’s digit” in the square of the following numbers?
(i) 1234 (ii) 26387 (iii) 52698
(iv) 99880 (v) 21222 (vi) 9106
The square of which of the following numbers would be an odd number/an even number?
Why?
(i) 727 (ii) 158 (iii) 269 (iv) 1980
What will be the number of zeros in the square of the following numbers?
(i) 60 (ii) 400
How many natural numbers lie between 92 and 102? Between 112 and 122?
Find whether each of the following numbers is a perfect square or not?
(i) 121 (ii) 55 (iii) 81
(iv) 49 (v) 69
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