Prove That Square Root 11 is Irrational Using The Square Root Property

If you have studied mathematics, you must be familiar with the term square root and how to calculate them. However, if it’s been a long time since you haven’t been able to revise the concept and calculations related to square root then now is the time you must. Through this article, we will touch on all the aspects of square roots from their meaning to their calculation. Besides, this article will also bring you a very interesting observation that you might have never acknowledged before. You will get to learn how to prove that square root 11 is irrational using the square root property. Therefore, make sure that you read the article thoroughly so that you can revise the concepts that have over time gotten weak and also have an interesting takeaway. Now, without any further ado let’s quickly learn about the meaning of the square root.

What Is The Meaning Of Square Roots?

From the points below let’s increase our awareness about square roots and build a better understanding of them.

  • 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.

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How To Find The Square Root Of Any Number?

To calculate the square root of any number we can bring four methods into use. The names of the four methods are mentioned below.

  • Estimation Method
  • Long Division Method
  • Prime Factorization Method
  • Repeated Subtraction Method 

How To Prove That Square Root 11 is Irrational Using The Square Root Property?

From the points below let’s learn how to confirm the above observation by using the square root property.

  • Let us assume we have to find the root of a number “n”, and express it as √n. On multiplication of the root of a number to itself should give the original number. 
  • For instance, √11 on multiplication to itself should give the number 11. 
  • To ascertain that root 11 is an irrational number, we can attempt to find the square root by the division method and contradiction method.
  • Therefore, the square root of 11 will be an irrational number if the value of the square root of 11 is a number that has values after decimal that are non-terminating and non-repeating.
  • We can prove that root 11 is an irrational number by various methods. The value of √11 is 3.31662479036… As we know that a decimal number that is non-terminating and non-repeating is also irrational. 
  • The value of root 11 is also non-terminating and non-repeating. This fulfills the condition of √11 is an irrational number. Hence, √11 is an irrational number.

We hope this article adds to preexisting understanding and also provides you with an interesting takeaway. For more such interesting and informative articles stay tuned with us.

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