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

(i) We have, $$32 = 30 + 2$$

$$(32)^2 = (30 + 2)^2$$

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

$$= 30^2 + 30 \times 2 + 2 \times 30 + 2^2$$

$$= 900 + 60 + 60 + 4$$

$$= 1024$$

So we have $$(32)^2 = 1024$$

(ii)We have, $$35 = (30 + 5)$$

$$(35)^2 = (30 + 5)^2$$

$$= 30(30 + 5) + 5(30 + 5)$$

$$= (30)^2 + 30 \times 5 + 5 \times 30 + (5)^2$$

$$= 900 + 150 + 150 + 25$$

$$= 1225$$

So we have $$(35)^2 = 1225$$

(iii) We have, $$86 = (80 + 6)$$

$$86^2 = (80 + 6)^2$$

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

$$= (80)^2 + 80 \times 6 + 6 \times 80 + (6)^2$$

$$= 6400 + 480 + 480 + 36$$

$$= 7396$$

So we have, $$(86)^2 = 7396$$

(iv)We have, $$93 = (90+ 3)$$

$$93^2 = (90 + 3)^2$$

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

$$= (90)^2 + 90 \times 3 + 3 \times 90 + (3)^2$$

$$= 8100 + 270 + 270 + 9$$

$$= 8649$$

So we have, $$(93)^2 = 8649$$

(v) We have, $$71 = (70 + 1)$$

$$71^2 = (70 + 1)^2$$

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

$$= (70)2 + 70 \times 1 + 1 \times 70 + (1)2$$

$$= 4900 + 70 + 70 + 1$$

$$= 5041$$

So we have, $$(71)^2 = 5041$$

(vi)We have, $$46 = (40+ 6)$$

$$46^2 = (40 + 6)^2$$

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

$$= (40)^2 + 40 \times 6 + 6 \times 40 + (6)^2$$

$$= 1600 + 240 + 240 + 36$$

$$= 2116$$

So we have, $$(46)^2 = 2116$$