Register to reply 
Perfect square? 
Share this thread: 
#1
Jan708, 12:07 AM

P: 231

Is a perfect square only "perfect" if the root is a whole number? Or does the term just dictate that decimals must eventually terminate?
For instance: [tex]\displaystyle{\sqrt{59.29} = 7.7}[/tex] 


#2
Jan708, 12:30 AM

P: 1,756

http://en.wikipedia.org/wiki/Perfect_square
Thus a perfect square always has a square root that has no decimal expansion. 


#3
Jan708, 07:00 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,297

A number always has a "decimal expansion". Integers just happen to have all 0s after the decimal point! A "perfect square" is the square of an integer.
52.29 is NOT a perfect square. 


#4
Jan708, 11:30 AM

P: 688

Perfect square?
Though 5229 is a perfect square. If you have a rational number as the result of a root, then the thing inside the root is the square of a rational (in this case, (77/10)^2 = 5229/100), so there are two perfect squares involved somewhere. Other than these musings, all the replies above are, of course, right.



#5
Jan708, 11:33 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,297




#6
Jan708, 11:34 AM

P: 688

Arrgh! Sorry, I just magnified your typo. :D



#7
Jan708, 01:40 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,297

Ooops! The original post does say "59.29", not "52.29" so you were right and I was wrong. I hate when that happens!



Register to reply 
Related Discussions  
What would be the perfect representative of earth look like?  General Discussion  35  
Looking for Best References with OfftheShelf Exact Solutions to Einstein's Field Equations for Charged Perfect Fluids  General Physics  0  
Looking for Best References with OfftheShelf Exact Solutions to Einstein's Field Equations for Charged Perfect Fluids  General Physics  0  
Perfect Tense?  General Discussion  10  
Excess over square function  Set Theory, Logic, Probability, Statistics  0 