March 20, 2023

How to Find Square Root | Formula, Examples

Determining the square root of a number is a fundamental mathematical operation which has various real-life utilizations. The square root of an amount is the value that, when multiplied with itself, offers the initial number. In arithmetics, square roots are used in various fields, such as geometry, trigonometry, algebra, and calculus, to figure out complex equations, calculate distances, and figure out angles. In physics, square roots are applied to work out acceleration, force, and velocity. In finance, square roots are used to work out interest rates and investment returns.

In this blog, we will dwell into the formula for calculating the square root, such as how to figure out the square root of different numbers, and the importance of comprehending the concept of square roots. By mastering the concept of square roots and comprehending its functional uses, individuals can better their problem-solving skills and gain a detailed grasp of the complex functions of the world surrounding us.

Why is Finding Square Roots Important?

Finding square roots is an essential math theory that has many real-world uses in several domains. In physics, square roots are applied to calculate the speed and acceleration of moving objects, that is necessary for analyzing and designing mechanical systems.

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

In algebra and calculus, square roots are utilized to solve intricate equations and carry out sophisticated math functions. For Instance, in algebra, square roots are applied to factor polynomials and determine quadratic equations. In calculus, square roots are applied to determine limits and derivatives, which are crucial for solving complex problems in physics, engineering, and other domains.

Understanding the theory of square roots is a crucial step in mastering these mathematical theories and is required for success in several fields for example mathematics, physics, engineering, and finance. By comprehending how to calculate square roots and utilizing the knowledge to determine problems, people can improve their problem-solving abilities and gain a deeper understanding of the complex workings of the world around us.

Common Mistakes in Calculating Square Roots

Working out square roots might seem simple, yet it is easy to make errors. One common mistake is ignoring 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, that cannot be stated as a finite decimal or fraction. Consequently, it is essential to revise whether the given value is a perfect square before attempting to calculate its square root.

One more general mistake is forgetting to streamline the square root whenever possible. Such as, the square root of 50 can be streamled as the square root of 25 times the square root of 2. Streamline the square root makes the workings easier and lowers the chances of making mistakes.

Additionally, rounding mistakes can occur when working out the square root of a value utilizing a calculator. It is crucial to revise the end result by squaring it to ensure that it is accurate.

By being aware of these general errors and taking preventive measures to avoid them, people can enhance their accuracy when calculating square roots and enhance their problem-solving skills in several fields.

How to Determine Square Root

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

Square Root of n = √n

Where "n" depicts the number whose square root is being determined. To figure out the square root of a number, you can utilize a calculator or carry out the workings by hand.

Such as 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 will take the square root of 81, which is 9.

√81 = 9

When calculating the square root of a decimal number, you could utilize the same formula. For example, to find the square root of 2.25, you should take the square root of 2.25, that is 1.5.

√2.25 = 1.5

It is important to note that not every value posses a perfect square root. In those cases, the square root can be approximated applying many methods, such as the bisection approach or Newton's approach.


Finally, calculating the square root of a number is an essential math concept which has various real-life applications in multiple fields, involving physics, engineering, and finance. The ability to determine square roots is an essential ability to be successful in various fields of study, for example math, science, and technology.

By understanding the formula for determining square roots and exercise the workings of square roots of different values, individuals can gain a deeper understanding of the theory and enhance their problem-solving abilities. However, it is important to be conscious of general mistakes that can occur during the working process, for instance forgetting to simplify the square root and failing to revise if the given value is a perfect square.

If you need help understanding how to find square roots or any other mathematical concept, consider connecting with Grade Potential Tutoring. Our experienced teachers are available online or in-person to offer customized and effective tutoring services to help you be successful.

Whether you need guidance with basic mathematics or more advanced mathematical concepts, our teachers can provide the help you require to achieve your academic goals. Connect with us today to schedule a tutoring session and take your math skills to the next stage.