## Monday, September 29, 2008

### Miscellaneous thought for the day...

Is there any whole number with last digit = "7" which is a square of a whole number.

I.e.

aaaaaaa^2 = nnnnnnnn7

:)

Eugene Tan said...

No. Mathematically impossible, if the whole number is real.

Try this:

Unit digit of 1^2 and of 9^2 are both 1.
Unit digit of 2^2 and of 8^2 are 4.
Unit digit of 3^3 and 7^2 are 9.
Unit digit of 4^2 and 6^2 are 6.
Unit digit of 5^2 is 5.
Unit digit of 10^2 is 0.

Regardless of the number of the digits of the numbers being squared, the unit digit follows the above patterns.

Therefore, all perfect squares of a real number must end in either 0, 1, 4, 5, 6 or 9.

QED.

The probligo said...

Bother.

I was going to discover the same thing about nnnnnn3 next. Now you done gone spoild my world shaking discovery.

There goes my Nobel Prize!!

Eugene Tan said...

There is no Nobel for Mathematics, though it has an equivalent called the Field's Medal.

When I was an undergrad, my classmates and I called it the cookie medal, after the rather popular Mrs Field's cookies outlet in Singapore.

Al said...

Cripes! is my math rusty...