26MAY21WED

Look at this number: 13.
Find its square.
Reverse the given number. Find its square.
What do you observe?

Multiply 21978 by 4.
What do you observe?

1^3 = ?, 5^3 = ?, 3^3 = ?, 1^3+5^3+3^3 = ?
3^3 = ?, 7^3 = ?, 0^3 = ?, 3^3+7^3+0^3 = ?
3^3 = ?, 7^3 = ?, 1^3 = ?, 3^3+7^3+1^3 = ?
4^3 = ?, 0^3 = ?, 7^3 = ?, 4^3+0^3+7^3 = ?

1*9 + 1 + 9 = ?
2*9 + 2 + 9 = ?
3*9 + 3 + 9 = ?
4*9 + 4 + 9 = ?
5*9 + 5 + 9 = ?
6*9 + 6 + 9 = ?
7*9 + 7 + 9 = ?
8*9 + 8 + 9 = ?
9*9 + 9 + 9 = ?

1089*9 = ?
What do you observe?
Will this happen with 10989*9, 109989*9 and 1099989 also? Check.
(This pattern holds good for all numbers in which 10 and 89 are separated by any number of 9s.)







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