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Know About The Square Roots Of 6 & 3 & The Steps To Prove That They Are Irrational

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Square Roots Of 6 & 3

Looking for something interesting and informative to read from the world of mathematics? You have landed on the right page as here you get interesting and instructive topics to read from mathematics. Today’s article is about square roots. Now, you might be thinking that is a daily known and simple concept. However, do you know how to prove that the square roots of 6 and 3 are irrational? Good, if you do, and nothing to worry about as through this article you will learn the steps to prove that they are irrational. Besides the interesting observation, you will also brush on all the fundamentals of finding a square root. Therefore, make sure that you read the article thoroughly. Now, without any further ado, let’s get reading. 

What Is The Meaning Of Square Roots In Mathematics?

  • The terms squares and square roots can be considered particular exponents. 
  • The square root of any number can be understood as the factor of that number which, on multiplying by itself, gives the original number. 
  • Given that ‘a’ is the square root of ‘b’, it would simply signify that a × a = b. For instance, let’s take the number 9. When the number 3 is multiplied by itself, it gives 9 as the product. 
  • This can be represented as 3 × 3 or 3^2. Here, the exponent is 2, and we can refer to it as a square. 
  • Now, if you see ½ in the exponent, it is called the square root of the number. For example √(n × n) = √n^2 = n, where n is a positive integer.
  • The symbol ‘√’ is called radical and the number placed in the symbol is called the radicand.

What Are The Techniques To Find The Square Root?

When it comes to finding out square roots it is not a big task to find the square root of a number that is a perfect square. To calculate the square root of any number we can bring four methods into use. The names of the four methods are mentioned below.

  • Finding Square Root by Estimation Method
  • Finding Square Root by Long Division Method
  • Repeated Subtraction Method of Square Root
  • Finding Square Root by Prime Factorization Method

Here, one must understand that the first three methods can be suitably used for numbers that are perfect squares. While the fourth method, which is the long division method, can be used for any number whether it is a perfect square or not.

How To Prove That The Square Roots Of 6 & 3 Are Irrational?

  • We can prove that square root 6 is irrational by observing that with the value of √6,  we get a decimal number that does not terminate and terms are not repeating themselves after the decimal point. 
  • Thus, the value obtained for the root of 6 satisfies the condition of being a non-terminating and non-repeating decimal number that keeps extending further after the decimal point which makes √6 an irrational number. Hence, √6 is an irrational number.
  • Similarly, you can prove that square root 3 is irrational. √3 gives a decimal number and it keeps extending. Since it does not terminate or repeat after the decimal point, √3 is an irrational number. 

Now, that you know how to verify the irrationality of the √6 and √3 and learned the basics related to the process of finding a square root make sure to read more about how to verify the above observation using different techniques. For more such articles stay connected to us.

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