Question

Example 1: Find the square of the following numbers without actual multin
(1) 39
(1) 42

and written few square patterns
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Answer 1

Answer

$(i) \: 39 {}^{2} = (30 + 9) {}^{2} = 30(30 +9 ) + 9(30 + 9) \\ = 30 {}^{2} + 30 \times 9 + 9 \times 30 + 9 {}^{2} \\ = 900 + 270 + 270 + 81 = 1521 \\ (ii) \: 42 {}^{2} = (40 + 2) {}^{2} = 40(40 + 2) + 2(40 + 2) \\ = 40 {}^{2} + 40 \times 2 + 2 \times 40 + 2 {}^{2} \\ = 1600 + 80 + 80 + 4 = 1764$

Patterns of squares

$25 {}^{2} = 625 = (2 \times 3)hundreds + 25 \\ 35 {}^{2} = 1225 = (3 \times 4)hundreds + 25 \\ 75 {}^{2} = 5625 = (7 \times 8)hundreds + 25 \\ 125 {}^{2} = 15625 = (12 \times 13)hundreds + 15$

Answer 2

hope it is helpful to you