The Python Square Root Function – Real Python (2024)

Square Roots in Mathematics

In algebra, a square, x, is the result of a number, n, multiplied by itself: x = n²

You can calculate squares using Python:

>>> n = 5>>> x = n ** 2>>> x25

The Python ** operator is used for calculating the power of a number. In this case, 5 squared, or 5 to the power of 2, is 25.

The square root, then, is the number n, which when multiplied by itself yields the square, x.

In this example, n, the square root, is 5.

25 is an example of a perfect square. Perfect squares are the squares of integer values:

>>> 1 ** 21>>> 2 ** 24>>> 3 ** 29

You might have memorized some of these perfect squares when you learned your multiplication tables in an elementary algebra class.

If you’re given a small perfect square, it may be straightforward enough to calculate or memorize its square root. But for most other squares, this calculation can get a bit more tedious. Often, an estimation is good enough when you don’t have a calculator.

Fortunately, as a Python developer, you do have a calculator, namely the Python interpreter!

The Python Square Root Function

Python’s math module, in the standard library, can help you work on math-related problems in code. It contains many useful functions, such as remainder() and factorial(). It also includes the Python square root function, sqrt().

You’ll begin by importing math:

>>> import math

That’s all it takes! You can now use math.sqrt() to calculate square roots.

sqrt() has a straightforward interface.

It takes one parameter, x, which (as you saw before) stands for the square for which you are trying to calculate the square root. In the example from earlier, this would be 25.

The return value of sqrt() is the square root of x, as a floating point number. In the example, this would be 5.0.

Let’s take a look at some examples of how to (and how not to) use sqrt().

>>> math.sqrt(49)7.0

>>> math.sqrt(70.5)8.396427811873332

>>> 8.396427811873332 ** 270.5

>>> math.sqrt(0)0.0

>>> math.sqrt(-25)Traceback (most recent call last): File "<stdin>", line 1, in <module>ValueError: math domain error

Square Roots in the Real World

To see a real-world application of the Python square root function, let’s turn to the sport of tennis.

Imagine that Rafael Nadal, one of the fastest players in the world, has just hit a forehand from the back corner, where the baseline meets the sideline of the tennis court:

Now, assume his opponent has countered with a drop shot (one that would place the ball short with little forward momentum) to the opposite corner, where the other sideline meets the net:

How far must Nadal run to reach the ball?

You can determine from regulation tennis court dimensions that the baseline is 27 feet long, and the sideline (on one side of the net) is 39 feet long. So, essentially, this boils down to solving for the hypotenuse of a right triangle:

Using a valuable equation from geometry, the Pythagorean theorem, we know that a² + b² = c², where a and b are the legs of the right triangle and c is the hypotenuse.

Therefore, we can calculate the distance Nadal must run by rearranging the equation to solve for c:

You can solve this equation using the Python square root function:

>>> a = 27>>> b = 39>>> math.sqrt(a ** 2 + b ** 2)47.43416490252569

So, Nadal must run about 47.4 feet (14.5 meters) in order to reach the ball and save the point.

Conclusion

Congratulations! You now know all about the Python square root function.

You’ve covered:

• A brief introduction to square roots
• The ins and outs of the Python square root function, sqrt()
• A practical application of sqrt() using a real-world example

Knowing how to use sqrt() is only half the battle. Understanding when to use it is the other. Now, you know both, so go and apply your newfound mastery of the Python square root function!