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.
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
The squares of which of the following would be odd numbers?
(i) 431 (ii) 2826 (iii) 7779 (iv) 82004
Observe the following pattern and find the missing digits.
112 = 121
1012 = 10210
10012 = 1002001
1000012 = 1 ............. 2 ..............1
100000012 = ........................
Observe the following pattern and supply the missing number.
112 = 121
1012 = 10201
101012 = 102030201
10101012 = ........................
...........2 = 102030405030201
