Find the value of-i 822-182ii 1282-722iii 197 - 203iv 198 - 198-102 - 10296v 14-7 - 15-3vi 8-632-1-372

We shall use the identity (a b) (a+b)=a2 b2. (i) (82)2 (18)2=(82 18)(82+18)=(64)(100)=6400 (ii) (128)2 (72)2=(128 72)(128+72)=(56)(200)=11200 (iii) 197 # ...

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Byju's Answer

Standard VIII

Mathematics

Associative Property of Rational Numbers

Find the valu...

Question

Find the value of:
(i) (82)² − (18)²
(ii) (128)² − (72)²
(iii) 197 × 203
(iv) $\frac{198 \times 198 - 102 \times 102}{96}$
(v) (14.7 × 15.3)
(vi) (8.63)² − (1.37)²

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Solution

We shall use the identity (a-b) (a+b)=a² - b².

(i)
$(82)^{2} - (18)^{2} = (82 - 18) (82 + 18) = (64) (100) = 6400$

(ii)
$(128)^{2} - (72)^{2} = (128 - 72) (128 + 72) = (56) (200) = 11200$

(iii)
$197 \times 203 = (200 - 3) (200 + 3) = {(200)}^{2} - {(3)}^{2} = 40000 - 9 = 39991$

(iv)
$\frac{198 \times 198 - 102 \times 102}{96} = \frac{{(198)}^{2} - {(102)}^{2}}{96} = \frac{(198 - 102) (198 + 102)}{96} = \frac{(96) (300)}{96} = 300$

(v)
$(14.7 \times 15.3) = (15 - 0.3) \times (15 + 0.3) = (15)^{2} - (0.3)^{2} = 225 - 0.09 = 224.91$

(vi)
$(8.63)^{2} - (1.37)^{2} = (8.63 - 1.37) (8.63 + 1.37) = (7.26) (10) = 72.6$

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Similar questions

Find the values of
(i) $(82)^{2} - (18)^{2}$
(ii) $(128)^{2} - (72)^{2}$
(iii) $197 \times 203$
(iv) $\frac{198 \times 198 - 102 \times 102}{96}$
(v) $(14.7 \times 15.3)$
(vi) $(8.63)^{2} - (1.37)^{2}$