Have you ever wondered how the concept of squares and square roots, which you must have learned in your school days, are actually applied in real-life situations? From calculating the square-shaped garden to designing a skyscraper, squares and square roots have a plethora of applications in the real world.

In this article, we will explore 15 fascinating real-life applications of squares and square roots that are both practical and intriguing. Additionally, you will also get some strategies to help you comprehend this mathematical concept better, so you can apply it to your daily life with ease.

So, Like adjacent angles, and coordinate planes examples, let’s dive in and discover how squares and square roots can be used in the real world!

**Fascinating real-life applications of squares and square roots in everyday scenarios**

Here are a few examples of the application of square and square roots in various scenarios:

**1. Interior:**

** **In order to accurately plan and create a space, squares are used in architecture to measure the area of a room or building. Take this example, To decide how many tiles are needed for the floor, an architect must calculate the size of the room. Squaring the length and width of the space, i.e., 12 x 10 = 120 square feet, will yield the area if the room is 12 feet long and 10 feet broad.

**2. Building construction:**

** **Have you ever wondered about math use in construction? Squaring is one of the fundamental concepts of math in building construction that involves using a square to ensure that structures are built to exact measurements. For example, when building a wall, a builder may use a square to ensure that the corners are perfectly perpendicular. On the other hand, square roots are used to calculate the length of diagonal braces and other angled components that are necessary to maintain the structural integrity of a building.

**3. Finance:**

** **Stock market volatility, a metric of how much a stock’s price swings over time, is calculated in finance using square roots. The calculation entails taking the stock’s return variance and square rooting it. Investors can use this information to assess the risk of a particular investment, which helps them make educated investing decisions.

**4. Architecture: **

Squaring is a tool used in engineering to determine the natural frequency of structures like bridges and buildings. This frequency assists in predicting how the structure will react to different loads. For instance, a bridge exposed to strong winds or busy traffic may vibrate excessively due to its low natural frequency.

**5. Science:**

** **Several scientific calculations employ square roots, such as determining the velocity of a moving object, the amount of radiation absorbed by a material, or the intensity of sound waves. These calculations aid scientists in their understanding of nature and can be utilized to develop new technologies and cures.

**6. Statistics:**

In statistical analysis, squares and square roots are employed to determine variance and standard deviation. Standard deviation is the square root of the variance, which represents how far the data deviates from the mean. These metrics assist statisticians in analyzing data sets and making sound judgments based on their results.

**7. Geometry: **

Geometry employs squares and square roots to compute the area and perimeter of shapes, as well as to solve problems involving right triangles and other polygons. The Pythagorean theorem, for example, involves calculating the length of the third side by squaring the lengths of the first two sides of a right triangle.

**8. Computer Science:**

** **Squares and square roots are used in computer programming for a variety of applications such as encryption algorithms, image processing, and game physics. Encryption algorithms, for example, use modular arithmetic and square roots to generate public and private keys used to secure data transmissions.

**9. Cryptography:**

Cryptography employs square roots in a variety of applications, including digital signatures, key exchange systems, and secure communication channels. Digital signatures, for example, use prime number and square root features to generate unique digital fingerprints that are used to authenticate data transactions.

**10. Navigation: **

Square roots are used in navigation to compute distances between points on a map or globe as well as to estimate a course’s bearing or direction. Pilots, for example, utilize square roots to compute the distance and direction between two points on a flight plan.

**11. Electrical Engineering: **

Electrical engineering uses square roots to compute power, voltage, and current in circuits, as well as to construct filters and other signal-processing devices. These computations are critical in the design and development of electrical systems like power grids, communication networks, and electronic devices.

**12. Cooking: **

Recipes often call for spices to be added in certain amounts per unit of volume. If you want to scale up the recipe, you need to adjust the amount of spice accordingly. To do this, maths is often used in cooking, you can use the square root of the scaling factor, which will help you maintain the right balance of flavors even when making larger batches.

**13. Photography: **

The aperture of a camera lens is a critical factor in controlling the amount of light that enters the camera. It is expressed as an f-number, which is the ratio of the focal length to the diameter of the aperture. The area of the aperture is proportional to the square of the f-number, which means that changing the f-number by a factor of two will change the amount of light entering the camera by a factor of four.

**14. Computer graphics:**

In many 2D and 3D graphics applications, squares and square roots are used in various calculations. For example, to calculate the distance between two points or the length of a vector, you need to use the Pythagorean theorem, which involves taking the square root of the sum of the squares of the coordinates.

**15. Telecommunication. **

Telecommunication often utilizes square and square roots. In wireless communication, the signal strength decreases as the distance from the transmitter increases. The decrease is proportional to the square of the distance, which is known as the inverse square law.

**Strategies to comprehend the concept of square and square roots better**

**Following are some tips to better understand the idea of squares and square roots:**

**Visualize the idea:**Squares and square roots are frequently simpler to comprehend when they are represented graphically. You may observe how the area of the larger square is related to the area of the smaller squares, for instance, by drawing a square and splitting it into smaller squares. You can better understand the subject by using tools and visual resources like charts, graphs, and diagrams.

**Practice with real-world examples:**Go through challenges using real-world events to improve your understanding of how squares and square roots are used in real-world situations. To put the idea into effect, you might determine the size of a square TV screen’s diagonal or the area of a rectangular room.

**Explain the concept in greater depth:**Squares and square roots can be difficult to understand, but by breaking them down into smaller components, they become more approachable. Learning the difference between a square and a square root, or how to compute a perfect square, for example, can help you understand the concept.

**Memorize the squares:**Learn the squares of the numbers 1 through 15 by heart. This will make it easier for you to solve problems using squares and square roots. For example, knowing that the square of 12 is 144 allows you to quickly calculate the square root of 144.

**Use online resources:**You can learn about and put the idea of squares and square roots to use by using the many online resources that are available. You can find videos, tutorials, interactive tools, quizzes, and any other mental math tools and resources to assist you in comprehending the idea in the way that is most comfortable for you.

**Conclusion**

The square and square root are important mathematical concepts with various applications in fields such as engineering, physics, finance, and computer science. It is important to teach students basic well to have a greater understanding and application of the concept in various scenarios. Use the above strategies to get a better grasp of the topic.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder ofSmartynote -‘The notepad app for dyslexia’,