Square Roots in Mathematics

In algebra, asquare,x, is the result of anumber,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 numbern, which when multiplied by itself yields the square,x.

In this example,n, the square root of 25, is 5.

25 is an example of aperfect 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 thePython interpreter!

The Python Square Root Function

Python’smath module in the standard library can help you work on math-related problems in code. It contains many useful functions, such asremainder() andfactorial(). It also includes thePython square root function,sqrt().

You’ll begin byimportingmath:

>>>importmath

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

sqrt() has a straightforward interface. It takes one parameter,x, which as you saw before, stands for the square you want to calculate the square root for. In the example from earlier, this would be25.

The return value ofsqrt() is the square root ofx, as afloating-point number. In the example, this would be5.0.

Next, you’ll take a look at some examples of how to usesqrt() and how not to usesqrt().

>>>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>", line1, in<module>ValueError:math domain error

Square Roots in the Real World

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

Imagine thatAlex de Minaur, one of the fastest players in the world, has just hit a forehand from the back corner, where the baseline meets the sideline of thetennis 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 fromregulation 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, thePythagorean theorem, you know thata² + b² = c², wherea andb are the legs of the right triangle andc is the hypotenuse.

Therefore, you can calculate the distance Nadal must run by rearranging the equation to solve forc:

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.

In this tutorial, you’ve covered:

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

Knowing how to usesqrt() is only part of the equation. Understanding when to use it is equally important. Now that you know both, go ahead and apply your newfound mastery of the Python square root function!

FAQs

You now have some experience with square roots in Python. Below, you’ll find a few questions and answers that sum up the most important concepts that you’ve covered in this tutorial.

You can use these questions to check your understanding or to recap and solidify what you’ve just learned. After each question, you’ll find a brief explanation hidden in a collapsible section. Click theShow/Hide toggle to reveal the answer.