Find the square of the following numbers
(i) 32 (ii) 35
(iii) 86 (iv) 93
(v) 71 (vi) 46
(i) 322 = (30 + 2)2
= 30 (30 + 2) + 2 (30 + 2)
= 302 + 30 x 2 + 2 x 30 + 22
= 900 + 60 + 60 + 4
= 1024
(ii) The number 35 has 5 in its unit's place. Therefore,
352 = (3) (3 + 1) hundreds + 25
= (3 x 4) hundreds + 25
= 1200 + 25 = 1225
(iii) 862 = (80 + 6)2
= 80 (80 + 6) + 6 (80 + 6)
= 802 + 80 x 6 + 6 x 80 + 62
= 6400 + 480 + 480 + 36
= 7396
(iv) 932 = (90 + 3)2
= 90 (90 + 3) + 3 (90 + 3)
= 902 + 90 x 3 + 3 x 90 + 32
= 8100 + 270 + 270 + 9
= 8649
(v) 712 = (70 + 1)2
= 70 (70 + 1) + 1 (70 + 1)
= 702 + 70 x 1 + 1 x 70 + 12
= 4900 + 70 + 70 + 1
= 5041
(vi) 462 = (40 + 6)2
= 40 (40 + 6) + 6 (40 + 6)
= 402 + 40 x 6 + 6 x 40 + 62
= 1600 + 240 + 240 + 36
= 2116