Squaring anumber in its 50s

[chrisstone]

I have to be honest this is not my idea, but one I saw on my itouch apps called 'Math Trick'. I have just made it into a flipchart, personally I think its well cool and I have never seen it before, see what you think.
Chris:cool:
54 squared = 2916

25 + 4 = 29
4 x 4 = 16
answer 2916
See if you can find some others or prove it algebraically....:confused:

[rexboggs5]

Great puzzle!
The rules are:
(1) Add 25 to the units digit
(2) Square the units digit
(3) Put these two answers together (the fancy term is to 'concatenate')

To prove this works using algebra:
The number can be represented as (50 + a) where 'a' is a number between 0 and 9 inclusive.
The square of the number is (50 + a)^2
Expanding gives (50 + a)^2 = 2500 + 100a + a^2
Re-arranging: 2500 + 100a + a^2 = 100(25 + a) + a^2

So the "hundreds place" is 25 + a (which is Step 1)
The "units place" is a^2 (which is Step 2)
Adding them gives the answer.

An example might help to clarify this: 54^2 = ?
25 + 4 = 29, so the answer has 29 hundreds.
4^2 = 16, so the answer as 16 units.
So the answer is 29 hundreds + 16 units = 2900 + 16 = 2916



Such puzzles as this one are wonderful applications of early algebra.

See the attached flp for another cool puzzle that can be explained using simple algebra. Once you open it, click on the crystal ball to launch the flash app. Then follow the instructions. Prepare to be amazed!

For the mathematically minded - use algebra to figure out how it works!


Cheers

Rex

[mrjdallen]

WOW I WAS IMPRESSED