Trick 24 : Squaring a 2-digit number beginning with 1

 Squaring a 2-digit number beginning with 1

Take a 2-digit number beginning with 1.

Square the second digit
(keep the carry) _ _ X

Multiply the second digit by 2 and
add the carry (keep the carry) _ X _

The first digit is one
(plus the carry) X

Example:

If the number is 16, square the second digit:
6 × 6 = 36 _ _ 6

Multiply the second digit by 2 and
add the carry: 2 × 6 + 3 = 15 _ 5 _

The first digit is one plus the carry:
1 + 1 = 2 2 _ _

So 16 × 16 = 256.



See the pattern?

For 19 × 19, square the second digit:
9 × 9 = 81 _ _ 1

Multiply the second digit by 2 and
add the carry: 2 × 9 + 8 = 26 _ 6 _

The first digit is one plus the carry:
1 + 2 = 3 3 _ _

So 19 × 19 = 361.