Find the square of the following numbers(i) 32 (ii) 35 (iii) 86 (iv) 9

1.	Find the square of the following numbers(i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46
Answer» (i) 32² = (30 + 2)² = 30 (30 + 2) + 2 (30 + 2) = 302 + 30 × 2 + 2 × 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 × 4) hundreds + 25 = 1200 + 25 = 1225 (iii) 86² = (80 + 6)² = 80 (80 + 6) + 6 (80 + 6) = 802 + 80 × 6 + 6 × 80 + 6² = 6400 + 480 + 480 + 36 = 7396 (iv) 93² = (90 + 3)² = 90 (90 + 3) + 3 (90 + 3) = 902 + 90 × 3 + 3 × 90 + 3² = 8100 + 270 + 270 + 9 = 8649 (v) 71² = (70 + 1)² = 70 (70 + 1) + 1 (70 + 1) = 702 + 70 × 1 + 1 × 70 + 1² = 4900 + 70 + 70 + 1 = 5041 (vi) 46² = (40 + 6)² = 40 (40 + 6) + 6 (40 + 6) = 402 + 40 × 6 + 6 × 40 + 6² = 1600 + 240 + 240 + 36 = 2116

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

Answer»

(i) 32² = (30 + 2)²

= 30 (30 + 2) + 2 (30 + 2)

= 302 + 30 × 2 + 2 × 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 × 4) hundreds + 25

= 1200 + 25 = 1225

(iii) 86² = (80 + 6)²

= 80 (80 + 6) + 6 (80 + 6)

= 802 + 80 × 6 + 6 × 80 + 6²

= 6400 + 480 + 480 + 36

= 7396

(iv) 93² = (90 + 3)²

= 90 (90 + 3) + 3 (90 + 3)

= 902 + 90 × 3 + 3 × 90 + 3²

= 8100 + 270 + 270 + 9

= 8649

(v) 71² = (70 + 1)²

= 70 (70 + 1) + 1 (70 + 1)

= 702 + 70 × 1 + 1 × 70 + 1²

= 4900 + 70 + 70 + 1

= 5041

(vi) 46² = (40 + 6)²

= 40 (40 + 6) + 6 (40 + 6)

= 402 + 40 × 6 + 6 × 40 + 6²

= 1600 + 240 + 240 + 36

= 2116