Question

show that 5√6 is an irrational number

Answer 1

this is the solution

Answer 2

Proving of $5\sqrt{6}$ is an irrational number.

Step-by-step explanation:

1. Let $5\sqrt{6}$ is an rational number (R).

     

   So

        $5\sqrt{6}$= R       ...1)

        $\sqrt{6}=\frac{R}{5}$      ...2)

     

2.  As we know that

  Sum of two rational number is an rational number.

   Subtraction of two rational number is an rational number.

   Multiplication of two rational number is an rational number.

   Division of two rational number is an rational number.       ...3)

3. As 5 is an rational number.

         R is an rational number as per our assumption.

    So Ratio of two rational number is also an rational number.

4. Means

   $\frac{R}{5}$ is an rational number.

  Then

  $\sqrt{6}$ is also an rational number.        ...4)

5. But$\sqrt{6}$ is an irrational number.

  So this is cause of wrong statement of equation 4).

  If equation 4) is wrong, equation 2) is also wrong.

 Similarly

   If equation 2) is wrong, equation 1) is also wrong.

means our assumption is wrong.

6. If a real number is not rational number, it must be an irrational number.