Question

prove that 3root 6 is not rational number​

Answer 1

Answer:

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Answer 2

Answer:

Let 3√6 be a rational number , say p / q where q ≠ 0. Then q > 1 because if q = 1 then p / q will be an integer , and there is no integer between 1 and 2 . So, p3 / q is a fraction different from an integer . This contradiction proves the result .

Step-by-step explanation:

Let 3√6 be a rational number , say p / q where q ≠ 0.

Then 3√6  = p / q  

Since 13 = 1, and 23 = 8, it follows that 1 < p / q  < 2

Then q > 1 because if q = 1 then p / q will be an integer , and there is no integer between 1 and 2 .

Now, 6 (p / q)3  

6 = p3 / q3

6q2 = p3 / q

q being an integer , 6q2 is an integer , and since q > 1 and q does not have a common factor with p and consequently with p3

So,  p3 / q is a fraction different from an integer .

Thus  6q2 ≠ p3 / q  

This contradiction proves the result .

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