How can I test if a number is a square number in Python?

Question

My code is

if graph == square_grid and type(math.sqrt(nodes)) is not int: 
    print "Your netork can't have that number of nodes"

Of course this doesn't work because math.sqrt always returns a float. How can I do this?

score 13 · Answer 1 · answered May 07 '13 at 18:50

13

One way is

int(math.sqrt(x)) ** 2 == x

answered May 07 '13 at 18:50

Fred Foo

score 7 · Answer 2 · answered May 07 '13 at 18:52

7

Because math.sqrt always returns a float, you can use the built in is_integer method

def is_square(x):
    answer = math.sqrt(x)
    return answer.is_integer()

this will return True if x is a square and False if it's not

>>> is_square(25)
True
>>> is_square(14)
False

answered May 07 '13 at 18:52

Ryan Saxe

Hm. Seeing as floating point numbers are imprecise, could it happen that the sqrt() of a square number will end up not being an integer because of rounding errors during the computation? That would make @larsmans's answer better. – millimoose May 07 '13 at 18:54
that is a valid point, although I just ran a for loop that would print out all valid squares up to 100,000 using this method, and it didn't miss one. – Ryan Saxe May 07 '13 at 19:04
Integers are exactly represented in floating point (they have all zeros after the point). I'm not sure whether `sqrt` is guaranteed to preserve that, though. – Fred Foo May 07 '13 at 19:18

score 1 · Answer 3 · answered May 07 '13 at 18:52

1

try:

math.sqrt(nodes) == int(math.sqrt(nodes))

answered May 07 '13 at 18:52

Christian Geier

this won't work, because of the imprecision of floats. If the difference between `math.sqrt(nodes)` and `int(math.sqrt(nodes))` is larger than `sys.float_info.epsilon` then you're out of luck. – MattDMo May 07 '13 at 19:06
do you mean _smaller_ than `sys.float_info.epsilon`? otherwise I'm confused… – Christian Geier May 07 '13 at 19:19
Larger. If the difference is larger than the epsilon, the system sees them as not equal, and the expression returns `False`. – MattDMo May 07 '13 at 20:35

score 0 · Answer 4 · answered Oct 17 '22 at 11:28

Using pure maths (no libraries) a square number can be determined in Python as follows:

not n**0.5 % 1

As the square root of a square integer is an integer, this test uses modulo 1 equal to zero to test if the square root is an integer.

The following will print the first five square numbers:

for i in range(1, 26):
    if not i**0.5 % 1:
        print(i)

Output:

4 Answers4