Perfect squares under 10,000

[fecoupefe]

Hello...


Question is how many perfect squares are less than 10,000.

I believe the answer is 99, but I can't figure out how to get there.

I believe perfect squares are 1,4,9,16,25,36,49,64,81 and 100.

Thanks for reading.

 

[Deleted member 4993]

Hello...


Question is how many perfect squares are less than 10,000.

I believe the answer is 99, but I can't figure out how to get there.

I believe perfect squares are 1,4,9,16,25,36,49,64,81 and 100.

Thanks for reading.

Why not include

$\displaystyle 32^2 \, = \, 1024 < 10000$

$\displaystyle 40^2 \, = \, 1600 < 10000$

$\displaystyle 50^2 \, = \, 2500 < 10000$

$\displaystyle 99^2 \, = \, 9801 < 10000$

 

[Denis]

Question is how many perfect squares are less than 10,000.

Since 100^2 = 10000, then obviously 99 is answer.

 

[mmm4444bot]

With so many references (on-line and in print) stating the definition of a perfect square as "any number that has a rational number as its square root", one could argue that there are an infinite number of perfect squares less than 10,000.

 

[Denis]

Re:

.... one could argue that there are an infinite number of perfect squares less than 10,000.

as long as the "one" who argues is YOU, I agree

 

[Deleted member 4993]

Re:

With so many references (on-line and in print) stating the definition of a perfect square as "any number that has a rational number as its square root", one could argue that there are an infinite number of perfect squares less than 10,000.

A square number, also called a perfect square, is a figurate number of the form S[sub:1v95k3r0]n[/sub:1v95k3r0] = n[sup:1v95k3r0]2[/sup:1v95k3r0], where n is an integer. The square numbers for , 1, ... are 0, 1, 4, 9, 16, 25, 36, 49, ... (Sloane's A000290).

from:

http://mathworld.wolfram.com/SquareNumber.html

Since perfect square is restricted to squares of integers - according to Wolfram (now who is going to argue with him?) - then we have finite numbers of perfect squares within a given finite domain.

 

[mmm4444bot]

… as long as the "one" who argues is YOU, I agree …

I will never start such an argument because I know the definition of a perfect square.

I just wanted to point out yet another example of pervasive academic misinformation. The current introductory algebra text used at Seattle Central Community College contains this misinformation, as well as two other texts in my own library.

I've seen it on-line at "math" sites often enough to remember, too. Easy to find. Here's one at icoachmath.com; their motto is "Leading to Excellence in Math".

 

[arthur ohlsten]

no.    no squared
1             1
2            4
3            9
4           16
.
.
.
100      10000

100 perfect squares up to 10,000, then 99 perfect squares below 10,000.
You are right

Arthur