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Question -

Find the square of the following numbers.
(i) 32
(ii) 35
(iii) 86
(iv) 93
(v) 71
(vi) 46



Answer -

(i)32 = 30 + 2
(32)
2 = (30 + 2)2
= 30(30 + 2) + 2(30 + 2)
= 30
2 + 30 × 2 + 2 × 30+ 22
= 900 + 60 + 60 + 4
= 1024
Thus (32)
2 = 1024

(ii)35 = (30 + 5)
(35)
2 = (30 + 5)2
= 30(30 + 5) + 5(30 + 5)
= (30)
2 + 30 × 5 + 5 × 30+ (5)2
= 900 + 150 + 150 + 25
= 1225
Thus (35)
2 = 1225

(iii)86 = (80 + 6)
86
2 = (80 + 6)2
= 80(80 + 6) + 6(80 + 6)
= (80)
2 + 80 × 6 + 6 × 80+ (6)2
= 6400 + 480 + 480 + 36
= 7396
Thus (86)
2 = 7396

(iv)93 = (90+ 3)
93
2 = (90 + 3)2
= 90 (90 + 3) + 3(90 + 3)
= (90)
2 + 90 × 3 + 3 × 90+ (3)2
= 8100 + 270 + 270 + 9
= 8649
Thus (93)
2 = 8649

(v)71 = (70 + 1)
71
2 = (70 + 1)2
= 70 (70 + 1) + 1(70 + 1)
= (70)
2 + 70 × 1 + 1 × 70+ (1)2
= 4900 + 70 + 70 + 1
= 5041
Thus (71)
2 = 5041

(vi)46 = (40+ 6)
46
2 = (40 + 6)2
= 40 (40 + 6) + 6(40 + 6)
= (40)
2 + 40 × 6 + 6 × 40+ (6)2
= 1600 + 240 + 240 + 36
= 2116
Thus (46)
2 = 2116

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