Trick 30 : Squaring a 2-digit number ending in 4

Squaring a 2-digit number ending in 4
Take a 2-digit number ending in 4.

Square the 4; the last digit is 6: _ _ _ 6
(keep carry, 1.)

Multiply the first digit by 8 and add the carry (1);
the 2nd number will be the next to the last digit:
_ _ X 6 (keep carry).

Square the first digit and add the carry: X X _ _.

Example:

If the number is 34, 4 × 4 = 16 (keep carry, 1);
the last digit is _ _ _ 6.

8 × 3 = 24 (multiply the first digit by 8), 24 + 1 = 25
(add the carry):
the next digit is 5: _ _ 5 6. (Keep carry, 2.)

Square the first digit and add the carry, 2: 1 1 5 6.

So 34 × 34 = 1156.



See the pattern?

For 84 × 84, 4 × 4 = 16 (keep carry, 1);
the last digit is _ _ _ 6.

8 × 8 = 64 (multiply the first digit by 8),
64 + 1 = 65 (add the carry):
the next digit is 5: _ _ 5 6. (Keep carry, 6.)

Square the first digit and add the carry, 6: 7 0 5 6.

So 84 × 84 = 7056.