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


6