Using identities, evaluate $78 x 82$

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Solution

To Evaluate : $78 x 82$
$78$ can be written as $(80 - 2)$ and $82$ can be written as $(80 + 2)$
$78 x 82 = (80 - 2) (80 + 2)$
Using the identity
$(a + b) (a - b) = a^{2} - b^{2}$
$\begin{array}{rcl} (80 - 2) (80 + 2) & = & {(80)}^{2} - {(2)}^{2} (80 - 2) (80 + 2) = 6400 - 4 \\ (80 - 2) (80 + 2) & = & 6396 \\ ∴ 78 x 82 & = & 6396 \end{array}$

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{5.2}^{2}

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{8.9}^{2}

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Using identities, evaluate.

(i) 71² (ii) 99² (iii) 102² (iv) 998²

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(viii) 8.9² (ix) 1.05 × 9.5

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78 \times 82

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