square of numbers in 100's

> Choose a number over 100 (START WITH SMALLER NUMBER).
> The last two places will be the square of
the last two digits (keep if any carry) _ _ _ X X.
> The first three places will be the number plus
the last two digits plus any carry: X X X _ _.

here is an Example:

> let the number be 108:
2. Square the last two digits (no carry): 8 × 8 = 64: _ _ _ 64
3. Add the last two digits to the number: 108 + 08= 116:
so 1 1 6 _ _
4. So 108 × 108 = 11664.

FIND SQUARE OF NUMBERS IN 200 TO 299

steps to find square of numbers in 200's

> Choose a number in the 200s (start with numbers under 210, then try for larger ones).
>The first digit of the square is 4: 4 _ _ _ _
> The next two digits will be 4 times the last 2 digits: _ X X _ _
> The last two places will be the square of the last digit: _ _ _ X X

here we take an Example:

> let the number be 207:
> The first digit is 4
so 4 _ _ _ _
> The next two digits are 4 times the last digit:
4 × 7 = 28
so _ 2 8 _ _
Square the last digit: 7× 7 = 49
so _ _ _ 49
So finally we get 206 × 206 = 42849.

and For larger numbers work right to left:

> Square the last two digits (keep the carry): _ _ _ X X
> 4 times the last two digits + carry: _ X X _ _
> Square the first digit + carry: X _ _ _ _

example

>If the number to be squared is 225:
> Square last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ 2 5
> 4 times the last two digits + carry:
4x25 = 100; 100+6 = 106 (keep 1): _ 0 6 _ _
> Square the first digit + carry:
2x2 = 4; 4+1 = 5: 5 _ _ _ _
> So 225 × 225 = 50625.