Are you making an effort to find a solution to a quadratic equation? It’s possible that you need to figure out how long one of the sides of a right triangle is. Calculating the answers to these and other sorts of equations in a timely and accurate manner is facilitated by the sqrt() function, which is part of the Python programming language. At the conclusion of this article, you will have learned the following:
- What a square root is
How to use the Python square root function,
can be useful in the real world
Let’s plunge in! Stop for Python Coffee: You’ll be able to get back to working on your project in no time at all thanks to our straightforward and efficient method for locating the information you require.
Square Roots in Mathematics
In algebra, a square, denoted by the letter x, is the product that is obtained when a number, denoted by the letter n, is multiplied by itself: x = n²
You may calculate squares using
>>> n = 5 >>> x = n ** 2 >>> x 25
For the purpose of computing a number’s power, the ** operator in Python is utilized. In this instance, the answer to the question is 25, which can also be written as 5 squared.
The number n, which, when multiplied by itself, results in the square x, is what we mean when we talk about the square root of a number.
The value of n, often known as the square root, is 5 in this illustration.
The number 25 is an illustration of a perfect square. The squares of integers are known as perfect squares.
>>> 1 ** 2 1 >>> 2 ** 2 4 >>> 3 ** 2 9
When you were learning your multiplication tables in elementary algebra, it’s possible that some of these perfect squares were among the ones you committed to memory.
If you are given a little perfect square, it might not be too difficult to calculate or learn to remember its square root. This calculation, however, can become somewhat more laborious for the vast majority of other squares. When you don’t have access to a calculator, it’s often possible to get by with an estimate.
To your good fortune, as a Python programmer, you already possess a calculator in the form of the Python interpreter.
The Python Square Root Function
Working on mathematical issues in code can be made easier with the help of the math module, which is part of the standard library. It includes a wide variety of helpful functions, such as the factorial() and remainder() routines. In addition to that, it features the square root function in Python.
You will start by bringing in the mathematics.
>>> import math
That’s all there is to it! Calculating square roots is now possible through the usage of the math.sqrt() function.
The sqrt() function has a very simple user interface.
It requires only one parameter, which is denoted by the letter x and, as you have seen before, represents the square whose square root you are attempting to compute. In the previous illustration, this would be equal to the number 25.
The square root of x is represented as a floating point number in the result that is returned by the sqrt() function. In the given scenario, this would be a score of 5.0.
Let’s take a look at some instances of how to use sqrt correctly (and incorrectly), shall we?()
The Square Root of a Positive Number
A positive number is one of the types of arguments that can be passed to the sqrt() function. This encompasses both integral and floating point data types.
For instance, you can determine the square root of 49 by using the notation sqrt.()
>>> math.sqrt(49) 7.0
The value that is returned is a floating point number and it is 7.0, which is the square root of 49.
You are able to pass float values in addition to integer values.
>>> math.sqrt(70.5) 8.396427811873332
Calculating its value allows you to confirm that the square root that was given to you was accurate.
>>> 8.396427811873332 ** 2 70.5
The Square Root of Zero
Even passing in 0 as a square to the Python square root function is OK.
>>> math.sqrt(0) 0.0
You usually won’t have to calculate the square root of zero very often, but you might be supplying a variable to sqrt() whose value you aren’t entirely sure of. This could be the case. Therefore, it is comforting to learn that it can deal with zero in those
The Square Root of Negative Numbers
It is impossible for any real number’s square to have a negative value. This is due to the fact that it is mathematically impossible to have a negative product unless one of the factors is positive and the other is negative. Because the product of a number and the number itself constitutes a square, it is logically impossible to have a negative real square.
>>> math.sqrt(-25) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: math domain error
If you try to give the sqrt() function a negative number as an argument, you will receive a ValueError. This is because negative values do not fall inside the realm of the available real squares. Instead, the square root of a negative number would have to be complex, which goes beyond the capabilities of Python’s built-in square root function.
Square Roots in the Real World
Let’s talk about tennis because it’s a great example of how the square root function in Python may be applied in the real world.
Imagine that Rafael Nadal, one of the most talented and fastest players in the world, has just hit a forehand from the back corner of the tennis court, where the baseline meets the sideline:
Now, let’s say that his rival has responded by taking a drop shot (a shot that would land the ball short with very little forward velocity) to the other corner, where the other sideline meets the net:
How far does Nadal need to run in order to get to the ball?
According to the dimensions of a standard tennis court, the length of the baseline is 27 feet, and the length of the sideline (on one side of the net) is 39 feet. Therefore, in order to find the length of the hypotenuse of a right triangle, we must perform the following calculation:
We know that a2 + b2 = c2 by using a useful equation from geometry called the Pythagorean theorem. In this equation, a and b are the legs of the right triangle, and c is the hypotenuse.
As a result, we are able to determine the required distance that Nadal must cover by rearranging the equation in order to find the value for c:
You can get a solution to this equation by utilizing the square root function in Python.
>>> a = 27 >>> b = 39 >>> math.sqrt(a ** 2 + b ** 2) 47.43416490252569
Therefore, in order for Nadal to reach the ball and rescue the point, he will need to sprint around 47.4 feet (14.5 meters).