Squaring a 2-digit number ending in 4

Steps
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 secondnumber will be the next to the last digit: __X6 (keep carry).
square the first digit and add the carry: XX__.

Example
if the number is 34, 4 x 4 =16 (keep carry, 1); the last digit is ___6.
8 x 3 = 24 (multiply the first digit by 8), 24 + 1 = 25 (add the carry): the next digit is 5: __56. (keep carry, 2).
square the first digit and add the carry, 2: 1156.
so 34 x 34 =1156.

Squaring a 2-digit ending in 3

Steps
take a 2-digit number ending in 3.
the last digit will be ___9.
multiply the first digit by 6: the second number will be the next to the last digit: __X9.
square the first digit and add the number carried from the previous step: XX__.

Example
if the number is 43, the last digit
is ___9.
6 x 4 = 24: __49.
4 x 4 = 16, 16 + 2 = 18 (add carry): 1849.
so 43 x 43 = 1849

Squaring a 2-digit number ending in 2

Steps
take a 2-digit number ending in 2.
the last digit will be ___4.
multiply the first digit by 4: the second number will be the next to the last digit: __X4.
square the first digit and add the number carried from the previous step: XX__.

Example
if the number is 52, the last digit is ___4.
4 x 5 = 20 : __04.
5 x 5 = 25, 25 + 2 = 27 (add carry): 2704.
so 52 x 52 = 2704.