Find the value of -ii frac 198 198-102 imes 10296 Choose the correct answers from the given options-

The correct options are A 8 C 300(i)6.25 × 6.25 1.75/4.5=(6.25)^2 (1.75)^2/4.5 Using identity, a^2 b^2 =(a b)(a+b) a=6.25 and b =1.75 =(6.25 1.75)(6.25+1.75)/4 ...

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Standard VIII

Mathematics

Algebraic Quadratic Identity

Find the valu...

Question

Find the value of :
$(i) \frac{6.25 \times 6.25 - 1.75 \times 1.75}{4.5} (i i) \frac{198 \times 198 - 102 \times 102}{96}$
Choose the correct answers from the given options .

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100

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300

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Solution

The correct options are
A 8
C 300
$(i) \frac{6.25 \times 6.25 - 1.75}{4.5} = \frac{(6.25)^{2} - (1.75)^{2}}{4.5}$
Using identity, $a^{2} - b^{2} = (a - b) (a + b)$
a=6.25 and b =1.75
$= \frac{(6.25 - 1.75) (6.25 + 1.75)}{4.5} = \frac{4.5 \times 8}{4.5} = 8$

$(i i) \frac{198 \times 198 - 102 \times 102}{96}$
Using identity, $a^{2} - b^{2} = (a - b) (a + b)$
Now,
$\frac{198^{2} - 102^{2}}{96} = \frac{(198 - 102) (198 + 102)}{96}$
$= \frac{96 \times 300}{96} = 300$

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\frac{198 \times 198 - 102 \times 102}{96}

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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) $(8.63)^{2} - (1.37)^{2}$

Q. Evaluate:

\frac{198 \times 198 - 102 \times 102}{96}

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Find the value of : (i)6.25×6.25−1.75×1.754.5(ii)198×198−102×10296 Choose the correct answers from the given options .

The correct options are A 8 C 300(i)6.25×6.25−1.754.5=(6.25)2−(1.75)24.5 Using identity, a2−b2=(a−b)(a+b) a=6.25 and b =1.75 =(6.25−1.75)(6.25+1.75)4.5=4.5×84.5=8 (ii)198×198−102×10296 Using identity, a2−b2=(a−b)(a+b) Now, 1982−102296=(198−102)(198+102)96 =96×30096=300

Find the value of :
$(i) \frac{6.25 \times 6.25 - 1.75 \times 1.75}{4.5} (i i) \frac{198 \times 198 - 102 \times 102}{96}$
Choose the correct answers from the given options .