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

Solution:

(i) 32 = 30 + 2

32² = (30 + 2)²

= (30 + 2)(30 + 2)

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

= 30² + 30 × 2 + 2 × 30 + 2²

= 900 + 60 + 60 + 4

= 1024

(ii) 35 = 30 + 5

35² = (30 + 5)²

= (30 + 5)(30 + 5)

= 30(30 + 5) + 5(30 + 5)

= 30² + 30 × 5 + 5 × 30 + 5²

= 900 + 150 + 150 + 25

= 1225

(iii) 86 = 80 + 6

86² = (80 + 6)²

= (80 + 6)(80 + 6)

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

= 80² + 80 × 6 + 6 × 80 + 6²

= 6400 + 480 + 480 + 36

= 7396

(iv) 93 = 90 + 3

93² = (90 + 3)²

= (90 + 3)(90 + 3)

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

= 90² + 90 × 3 + 3 × 90 + 3²

= 8100 + 270 + 270 + 9

= 8649

(v) 71 = 70 + 1

71² = (70 + 1)²

= (70 + 1)(70 + 1)

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

= 70² + 70 × 1 + 1 × 70 + 1²

= 4900 + 70 + 70 + 1

= 5041

(vi) 46 = 40 + 6

46² = (40 + 6)²

= (40 + 6)(40 + 6)

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

= 40² + 40 × 6 + 6 × 40 + 6²

= 1600 + 240 + 240 + 36

= 2116

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

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Video Solution:

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

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.2 Question 1

Summary:

Thus, the squares of the numbers (i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46 are (i) 1024, (ii) 1225, (iii) 7396, (iv) 8649, (v) 5041, (vi) 2116

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