Find the square of 1468 by writing this as 1465 + 3.

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Solution

(a + b)² = a² + 2ab + b²

∴1468² = (1465 + 3)² = 1465² + 2 × 1465 × 3 + 9 = 1465² + 8799

The number 1465 ends in 5.

Now, 146 × (146 + 1) = 21462

∴ 1465² = 2146225

∴ 1468² = 2146225 + 8799 = 2155024

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Find the square of 1468 by writing this as 1465 + 3.

(a + b)2 = a2 + 2ab + b2 ∴14682 = (1465 + 3)2 = 14652 + 2 × 1465 × 3 + 9 = 14652 + 8799 The number 1465 ends in 5. Now, 146 × (146 + 1) = 21462 ∴ 14652 = 2146225 ∴ 14682 = 2146225 + 8799 = 2155024

(a + b)² = a² + 2ab + b²

∴1468² = (1465 + 3)² = 1465² + 2 × 1465 × 3 + 9 = 1465² + 8799

The number 1465 ends in 5.

Now, 146 × (146 + 1) = 21462

∴ 1465² = 2146225

∴ 1468² = 2146225 + 8799 = 2155024