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