Question

Find the square of the following numbers without actual multiplication.
(i) 39
(ii) 42​

Answer 1

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(i) $\tt\longrightarrow{39^2\: =\: (30\: +\: 9\:)^2}$

⠀ $\tt\longrightarrow{30(30\: +\: 9)\: +\: 9(30\: +\: 9)}$

⠀ $\tt\longrightarrow{30^2\: +\: 30\: ×\: 9\: +\: 9\: 30\: +\: 9^2}$

⠀ $\tt\longrightarrow{900\: +\: 270\: +\: 270\: +\: 81}$

⠀ $\tt\longrightarrow{1521}$

⠀⠀

(ii) $\tt\longrightarrow{42^2\: =\: (40+2)^2}$

⠀ $\tt\longrightarrow{40(40\: +\: 2)\: +\: 2(40\: +\: 2)}$

⠀ $\tt\longrightarrow{40^2\: +\: 40\: ×\: 2\: +\: 2\: ×\: 40\: +\: 2^2}$

⠀ $\tt\longrightarrow{1600\: +\: 80\: +\: 80\: +\: 4}$

⠀ $\tt\longrightarrow{1764}$

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Answer 2

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( i ) 39^2

= (30 + 9)^2}

= (30+9)^2

= 30(30 + 9) + 9(30 + 9)

= 30^2 + 30 × 9 + 930 + 9^2

= 900 + 270 + 270 + 81

= 1521

( ii ) 42^2

= (40 + 2)^2

= 40(40 + 2) +2(40 + 2)

= 40^2 + 40 × 2 + 2 × 40 + 2^2

= 1600 + 80 + 80 + 4

= 1764

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⠀⭕Answers:-

⠀⠀⠀⠀⠀⭕( i ) 1521

⠀⠀⠀⠀⠀⠀⠀⠀⠀⭕( ii ) 1764

⠀⠀⠀⠀⠀⠀⠀❍Hope it helps :)