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3 Applications of Square and Square Roots in Daily Life

This article will talk about the squares and square roots and fun methods to learn about them. A square root of a number is defined as a value, when multiplied by itself, yields the original number. Examples of square roots are 9 = 3,16 = 4,25 = 5, etc. When we multiply 3 by itself, we get 9; thus, the square root of 9 is 3. Similarly, 4 is the square root of 16. We get the square of a number when we multiply the number by itself. For example, 3*3 = 32 = 9, 4*4 = 42 = 16 etc. Thus, the square of 3 is 9. So we can say that the square root of 9 is 3 whereas the square of 3 is 9. Based on the same concept, if we multiply the same number thrice, we get its cube. Example, 3*3*3 = 27. Also, the cube root of 27 will be 3. 


Between 1800 BC and 1600 BC, the Yale Babylonian Collection YBC 7289 clay tablet was created that spoke about the square root of two. A copy of the Rhind Mathematical Papyrus from 1650 BC shows how Egyptians used an inverse proportion method to extract square roots. In India, the Sulba Sutras that were dated around 800 – 500 BC used the knowledge of squares and squares roots. Good approximations of the square roots of 2 and 3 can be found in these texts. Greek and Chinese Mathematicians also conducted extensive research on these concepts as well as the irrationality of numbers. As time progressed, many extraordinary minds came together to give us the concept of square roots and squares as we know them today. 

Applications of Squares and Square Roots

  1. When you go to find a new apartment, you will want to know the size of it. Newspaper and online advertisements usually give the dimensions of the apartment by only listing its area, such as 625 square feet. This can become hard to visualize. However, if you use the concept of square roots and convert this number in the form of 25*25 square feet, it gives you a better idea of how big the apartment is. Using cube roots can provide a more precise dimension of the apartment. 
  2. Square roots are also used to find the period of a pendulum. 
  3. Squares and square roots are used in the Pythagoras theorem. Say you have an erect vertical pole, and you want to find the shadow it casts on the ground. By determining a few quantities and applying this theorem, you can quickly determine the length of the pole’s shadow on the ground. 

The concept of squares and square roots are used in all walks of life, such as carpentry, engineering, designing buildings, and technology. 

Methods to Study

  1. Practice Questions – To master this subject, it is highly recommended that you solve several practice sums. These questions should be wide-ranging and have an increasing level of difficulty. 
  2. Visual Aids – While studying any topic, it is best to use visual aids such as videos, movies, interactive apps, and simulations. This enables you to retain the concept faster and apply it easily to practical problems. 
  3. External help – It is best to avail the services of a reliable institution such as Cuemath to help with your studying process. Cuemath uses several resources to help students in developing strong foundational concepts in Mathematical topics. 


There are several applications of square roots in daily life. Hopefully, this article gave you an insight into the concept of squares and how to use them.