Using identities, evaluate $8 . 9^{2}$

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Solution

Evaluate: $8 . 9^{2}$
$8 . 9^{2}$ can be written as ${(9 - 0.1)}^{2}$
Using the identity ${(a - b)}^{2} = a^{2} + b^{2} - 2 ab$ we get,
$\begin{array}{rcl} {(8.9)}^{2} & = & {(9 - 0.1)}^{2} \\ {(8.9)}^{2} & = & 9^{2} + 0 . 1^{2} - 2 \times 9 \times 0.1 \\ {(8.9)}^{2} & = & 9^{2} + 0 . 1^{2} - 1.8 \\ {(8.9)}^{2} & = & 81 + 0.01 - 1.8 \\ {(8.9)}^{2} & = & 79.21 \\ ∴ 8 . 9^{2} & = & 79.21 \end{array}$

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Similar questions

{8.9}^{2}

71^{2}

99^{2}

102^{2}

998^{2}

{5.2}^{2}

297 \times 303

78 \times 82

{8.9}^{2}

1.05 \times 9.5

Using identities, evaluate.

(i) 71² (ii) 99² (iii) 102² (iv) 998²

(v) (5.2)² (vi) 297 × 303 (vii) 78 × 82

(viii) 8.9² (ix) 1.05 × 9.5

{8.9}^{2}

{8.9}^{2}

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