The Probligo: Miscellaneous thought for the day...

Monday, September 29, 2008

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.; 12:52 PM
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!!; 5:09 PM
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.; 10:42 PM
Al said...: Cripes! is my math rusty...; 5:48 PM