Prove that  
1
√11
  is an irrational number.


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Answer:


Step by Step Explanation:
  1. Let's assume  
    1
    √11
      is a rational number.
    Therefore, we can find two integers, a and b, such that,
     
    1
    √11
      =  
    a
    b
      [where, b is not equal to zero.]
  2. Now,
    √11 =  
    b
    a
     
     
    b
    a
      is a rational number as a and b are integers.
    Therefore, √11 is a rational which contradicts to the fact that √11 is Irrational.
    Hence, our assumption is false and  
    1
    √11
      is irrational.
  3. Therefore,  
    1
    √11
      is an irrational number.

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