March 20, 2023

How to Find Square Root | Formula, Examples

Calculating the square root of a figure is a basic mathematical function which has several real-life utilizations. The square root of a number is the value that, when multiplied with itself, offers the original number. In mathematics, square roots are used in various domains, such as geometry, trigonometry, algebra, and calculus, to figure out complicated equations, work out distances, and figure out angles. In physics, square roots are applied to calculate velocity, acceleration, and force. In finance, square roots are applied to work out interest rates and investment returns.

In this blog article, we will explore the formula for calculating the square root, such as how to find the square root of various numbers, and the significance of comprehending the concept of square roots. By conquering the concept of square roots and understanding its realistic uses, students can improve their problem-solving abilities and obtain a detailed understanding of the intricate functions of the world surrounding us.

Why is Determining Square Roots Essential?

Determining square roots is an important arithmetic concept which has many practical uses in various domains. In physics, square roots are utilized to figure out the speed and acceleration of moving objects, which is essential for designing and analyzing mechanical systems.

Engineers further apply square roots to work out the dimensions of structures and to determine the forces acting on them. In finance, square roots are utilized to determine interest rates and return on investment, that is important for making calculated financial decisions.

In algebra and calculus, square roots are used to determine complicated equations and perform advanced mathematical functions. For example, in algebra, square roots are utilized to factor polynomials and work out quadratic equations. In calculus, square roots are applied to work out derivates and limits, which are crucial for figuring out complicated problems in physics, engineering, and other domains.

Understanding the theory of square roots is an important step in conquering these arithmetical concepts and is required for success in various fields for example math, physics, engineering, and finance. By comprehending how to calculate square roots and using the knowledge to determine challenges, people can enhance their problem-solving skills and get a deeper understanding of the complex workings of the world around us.

Common Mistakes in Calculating Square Roots

Calculating square roots may look straightforward, but it is simple to make errors. One general error is forgetting to check if the given number is a perfect square or not. A perfect square is a number whose square root is an integer, for instance 4, 9, 16, 25, and so on. If the value is not a perfect square, it will have an irrational square root, which cannot be stated as a finite decimal or fraction. Consequently, it is essential to revise whether the provided number is a perfect square prior aiming to figure out its square root.

Another general error is forgetting to simplify the square root when possible. For example, the square root of 50 could be streamled as the square root of 25 times the square root of 2. Streamline the square root makes the workings simpler and decreases the chances of making mistakes.

Additionally, rounding errors can occur when working out the square root of a value employing a calculator. It is essential to check the outcome by squaring it to make sure that it is precise.

By being aware of these general errors and taking preventive measures to prevent them, people can increase their precision when determining square roots and enhance their problem-solving skills in numerous domains.

How to Calculate Square Root

The formula for finding the square root of a value is as follows:

Square Root of n = √n

Where "n" portrays the value whose square root is being determined. To figure out the square root of a value, you could utilize a calculator or perform the workings by hand.

For example, to find the square root of 25, you would take the square root of 25, which is 5.

√25 = 5

Likewise, to calculate the square root of 81, you should take the square root of 81, which is 9.

√81 = 9

When calculating the square root of a decimal number, you can utilize the same formula. For example, to find the square root of 2.25, you will take the square root of 2.25, which is 1.5.

√2.25 = 1.5

It is essential to keep in mind that not every value posses a perfect square root. In such situations, the square root could be approximated applying various techniques, such as the bisection approach or Newton's method.


In conclusion, finding the square root of a value is an essential math theory that has various practical uses in several fields, involving engineering, physics, and finance. The ability to find square roots is a necessary ability for success in many areas of study, for example math, science, and technology.

By getting a grasp of the formula for calculating square roots and exercise the calculation of square roots of various values, individuals can get a detailed understanding of the concept and better their problem-solving skills. But, it is crucial to be aware of common mistakes that can occur during the working process, such as forgetting to streamline the square root and failing to revise whether the given number is a perfect square.

Whether you need guidance understanding how to determine square roots or any other math theory, contemplate connect with us at Grade Potential Tutoring. Our adept instructors are accessible remotely or face-to-face to provide customized and productive tutoring services to guide you succeed.

If you need guidance with basic mathematics or further advanced mathematical concepts, our instructors can provide the help you need to reach your academic goals. Connect with us right now to plan a tutoring session and take your math skills to the next stage.