Using suitable algebraic identity, find the value of ${(4.9)}^{2}$ .

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24.25

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24.01

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Solution

The correct option is D 24.01
${(4.9)}^{2}$
= ${(5.0 - 0.1)}^{2}$

Using the identity: $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ we get
${(5.0 - 0.1)}^{2}$
= ${(5)}^{2}$ - $2 (5) (0.1)$ + ${(0.1)}^{2}$
= $25 + 0.01 - 1$
= $24.01$

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