Question

Find the square of the following numbers

1. 32
2. 35
3. 86
4. 93
5. 71
6. 46

Answer 1

(i) $32^2 = (30 + 2)^2$
= $30 (30 + 2) + 2 (30 + 2)$
= $30^2 + 30 \times 2 + 2 \times 30 + 2^2$
= $900 + 60 + 60 + 4$
= $1024$

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(ii) The number $35$ has $5$ in its unit's place.
Therefore,
$35^2 = (3) (3 + 1)$ hundreds + $25$
= $(3 \times 4)$ hundreds + $25$
= $1200 + 25 = 1225$

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(iii) $86^2 = (80 + 6)^2$
= $80 (80 + 6) + 6 (80 + 6)$
= $80^2 + 80 \times 6 + 6 \times 80 + 6^2$
= $6400 + 480 + 480 + 36$
= $7396$

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(iv) $93^2 = (90 + 3)^2$
= $90 (90 + 3) + 3 (90 + 3)$
= $90^2 + 90 \times 3 + 3 \times 90 + 3^2$
=$8100 + 270 + 270 + 9$
= $8649$

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(v) $71^2 = (70 + 1)^2$
= $70 (70 + 1) + 1 (70 + 1)$
= $70^2 + 70 \times 1 + 1 \times 70 + 1^2$
= $4900 + 70 + 70 + 1$
= $5041$

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(vi) $46^2 = (40 + 6)^2$
= $40 (40 + 6) + 6 (40 + 6)$
= $40^2 + 40 \times 6 + 6 \times 40 + 6^2$
= $1600 + 240 + 240 + 36$
= $2116$