What will be the unit digit of the squares of the following numbers?
(i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555
(i) ∵ 1 × 1 = 1
∴ The unit’s digit of (81 )2 will be 1.
(ii) ∵ 2 × 2 = 4
∴ The unit’s digits of (272)2 will be 4.
(iii) Since, 9 × 9 = 81
∴ The unit’s digit of (799)2 will be 1.
(iv) Since, 3 × 3 = 9
∴ The unit’s digit of (3853)2 will be 9.
(v) Since, 4 × 4= 16
∴ The unit’s digit of (1234)2 will be 6.
(vi) Since 7 × 7 = 49
∴ The unit’s digit of (26387)2 will be 9.
(vii) Since, 8 × 8 = 64
∴ The unit’s digit of (52698)2 will be 4.
(viii) Since 0 × 0 = 0
∴ The unit’s digit of (99880)2 will be 0.
(ix) Since 6 x 6 = 36
∴ The unit’s digit of (12796)2 will be 6.
(x) Since, 5 x 5 = 25
∴ The unit’s digit of (55555)2 will be 5.
Observe the following pattern and supply the missing number.
112 = 121
1012 = 10201
101012 = 102030201
10101012 = ........................
...........2 = 102030405030201
Observing the above, we have
(i)(1010101)2 = 1020304030201
(ii) 10203040504030201 = (101010101 )2
The squares of which of the following would be odd numbers?
(i) 431 (ii) 2826 (iii) 7779 (iv) 82004
Since the square of an odd natural number is odd and that of an even number is an even number.
∴ (i) The square of 431 is an odd number
(∵ 431 is an odd number)
(ii) The square of 2826 is an even nnumber.
(∵ 2826 is an odd number)
(iii) The square of 7779 is an odd number
(∵ 7779 is an odd number)
(iv) The square of 82004 is an even nnumber.
(∵ 82004 is an odd number)
Observe the following pattern and find the missing digits.
112 = 121
1012 = 10210
10012 = 1002001
1000012 = 1 ............. 2 ..............1
100000012 = ........................
Observing the above pattern, we have
(i) (100001)2 = 10000200001
(ii) (10000001)2 = 100000020000001
The following numbers are obviously not perfect squares. Give reason.
(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050
(i) 1057
Since, the ending digit is 7 (which is not one of 0, 1, 4, 5, 6 or 9)
∴ 1057 is not a perfect square.
(ii) 23453
Since, the ending digit is 7 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 23453 is not a perfect square.
(iii) 7928
Since, the ending digit is 8 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 7928 is not a perfect square.
(iv) 222222
Since, the ending digit is 2 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 222222 is not a perfect square.
(v) 64000
Since, the number of zeros is odd.
∴ 64000 is not a perfect square.
(vi) 89722
Since, the ending digits is 2 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 89722 is not a perfect square.
(vii) 222000
Since, the number of zeros is odd.
∴ 222000 is not a perfect square.
(viii) 505050
The unit’s digit is odd zero.
∴ 505050 can not be a perfect square.
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