Question

hello, my name is diya i am going to ask you a question it's just a quiz ....find the square of the following numbers without actual multiplication questions are 1 is 39 and 2nd is 42

Answer 1

1. by nikhilam sutra

42^2 = 4(39-1) / (-1)^2 base = 10

=4(38) / 1 sub base digit = 4

=152/1 sub base =4 × 10 =40

=1521 ans. deviation = -1

2. by nikhilam sutra

42^2 = 4(42+2) / (+2)^2 base = 10

= 4(44) / 4 sub base digit = 4

= 176 / 4 sub base =4 × 10 =40

= 1764 ans. deviation = +2

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Answer 2

$32 {}^{2} = (30 + 9) {}^{2} = 30(30 + 9) + 9(30 + 9) \\ = 30 {}^{2} + 30 \times 9 + 9 \times 30 + 9 {}^{2} \\ = 900 + 270 + 81 = 1521 \\ \\ 42 {}^{2} = (40 + 2) {}^{2} = 40(40 + 2) + 2(40 + 2) \\ = 40 {}^{2} + 40 \times 2 + 2 \times 0 + 2 {}^{2} \\ = 1600 + 80 + 80 + 4 = 1764$