Trick 27 : Squaring a 2-digit number ending in 1

Squaring a 2-digit number ending in 1
Take a 2-digit number ending in 1.

Subtract 1 from the number.

Square the difference.

Add the difference twice to its square.

Add 1.

Example:

If the number is 41, subtract 1: 41 - 1 = 40.

40 × 40 = 1600 (square the difference).

1600 + 40 + 40 = 1680 (add the difference twice
to its square).

1680 + 1 = 1681 (add 1).

So 41 × 41 = 1681.



See the pattern?

For 71 × 71, subtract 1: 71 - 1 = 70.

70 × 70 = 4900 (square the difference).

4900 + 70 + 70 = 5040 (add the difference twice
to its square).

5040 + 1 = 5041 (add 1).

So 71 × 71 = 5041.