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Squares and Square Roots
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08/08/2021 11:16 am
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Find the square of the following numbers.
(i) 32
(ii) 35
(iii) 86
(iv) 93
(v) 71
(vi) 46
1 Answer
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08/08/2021 11:20 am
(i) (32)2
= (30 + 2)2
= (30)2 + (2)2 + 2 × 30 × 2
[Since, (a + b)2 = a2 + b2 + 2ab]
= 900 + 4 + 120
= 1024
(ii) (35)2
= (30 + 5)2
= (30)2 + (5)2 + 2 × 30 × 5
[Since, (a + b)2 = a2 + b2 + 2ab]
= 900 + 25 + 300
= 1225
(iii) (86)2
= (90 – 4)2
= (90)2 + (4)2 – 2 × 90 × 4
[Since, (a + b)2 = a2 + b2 + 2ab]
= 8100 + 16 – 720
= 8116 – 720
= 7396
(iv) (93)2
= (90 + 3)2
= (90)2 + (3)2 + 2 × 90 × 3
[Since, (a + b)2 = a2 + b2 + 2ab]
= 8100 + 9 + 540
= 8649
(v) (71)2
= (70+1 )2
= (70)2 + (1)2 + 2 × 70 × 1
[Since, (a + b)2 = a2 + b2 + 2ab]
= 4900 + 1 + 140
= 5041
(vi) (46)2
= (50 -4 )2
= (50)2 + (4)2 – 2 × 50 × 4
[Since, (a + b)2 = a2 + b2 + 2ab]
= 2500 + 16 – 400
= 2116