299
Question
Mentally compute the squares of the numbers given below:
(i) 98
(ii) 198
(iii) 999
(iv) 1998
(v) 195
(vi) 9.7
Mentally compute the squares of the numbers given below:
(i) 98
(ii) 198
(iii) 999
(iv) 1998
(v) 195
(vi) 9.7
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Solution
We know that (x − y)2 = x2 + y2 − 2xy
(i)
98 = 100 − 2
⇒ (98)2 = (100 − 2)2
= (100)2 + 22 − 2 × 100 × 2
= 10000 + 4 − 400
= 9604
(ii)
198 = 200 − 2
⇒ (198)2 = (200 − 2)2
= (200)2 + 22 − 2 × 200 × 2
= 40000 + 4 − 800
= 39204
(iii)
999 = 1000 −1
⇒ (999)2 = (1000 −1)2
= (1000)2 + 12 − 2 × 1000 × 1
= 1000000 + 1 − 2000
= 998001
(iv)
1998 = 2000 − 2
⇒ (1998)2 = (2000 − 2)2
= (2000)2 + 22 − 2 × 2000 × 2
= 4000000 + 4 − 8000
= 3992004
(v)
195 = 200 − 5
⇒ (195)2 = (200 − 5)2
= (200)2 + 52 − 2 × 200 × 5
= 40000 + 25 − 2000
= 38025
(vi)
9.7 = 10 − 0.3
⇒ (9.7)2 = (10 − 0.3)2
= (10)2 + (0.3)2 − 2 × 10 × 0.3
= 100 + 0.09 − 6
= 94.09
We know that (x − y)2 = x2 + y2 − 2xy
(i)
98 = 100 − 2
⇒ (98)2 = (100 − 2)2
= (100)2 + 22 − 2 × 100 × 2
= 10000 + 4 − 400
= 9604
(ii)
198 = 200 − 2
⇒ (198)2 = (200 − 2)2
= (200)2 + 22 − 2 × 200 × 2
= 40000 + 4 − 800
= 39204
(iii)
999 = 1000 −1
⇒ (999)2 = (1000 −1)2
= (1000)2 + 12 − 2 × 1000 × 1
= 1000000 + 1 − 2000
= 998001
(iv)
1998 = 2000 − 2
⇒ (1998)2 = (2000 − 2)2
= (2000)2 + 22 − 2 × 2000 × 2
= 4000000 + 4 − 8000
= 3992004
(v)
195 = 200 − 5
⇒ (195)2 = (200 − 5)2
= (200)2 + 52 − 2 × 200 × 5
= 40000 + 25 − 2000
= 38025
(vi)
9.7 = 10 − 0.3
⇒ (9.7)2 = (10 − 0.3)2
= (10)2 + (0.3)2 − 2 × 10 × 0.3
= 100 + 0.09 − 6
= 94.09
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