Trick 37 : Squaring numbers made up of 3's

Squaring numbers made up of 3's
Choose a a number made up of threes.

The square is made up of: one fewer 1 than there are repeating 3's

zero

one fewer 8 than there are repeating 3's
(same as the 1's in the square)

nine.

Example:

If the number to be squabrown is 3333:

The square of the number has: three 1's (one fewer than
digits in number)                         1 1 1 _ _ _ _ _
next digit is 0                               _ _ _ 0 _ _ _ _
three 8's (same number as 1's)     _ _ _ _ 8 8 8 _
a final 9                                       _ _ _ _ _ _ _ 9



So 3333 × 3333 = 11108889.



See the pattern?

If the number to be squabrown is 333:

The square of the number has: two 1's           1 1 _ _ _ _ _
next digit is 0                                                 _ _ _ 0 _ _ _
two 8's                                                         _ _ _ _ 8 8 _
a final 9                                                        _ _ _ _ _ _ 9



So 333 × 333 = 110889.