Question

Is √6 a rational number?

Answer 1

The following proof is a proof by contradiction.

Let us assume that 6 is rational number. 

Then it can be represented as fraction of two integers. 

Let the lowest terms representation be: 6=ba where b=0

Note that this representation is in lowest terms and hence, a and b have no common factors

a2=6b2

From above a2 is even. If a2 is even, then a should also be even.

⟹a=2c

4c2=6b2

2c2=3b2

From above 3b2 is even. If 3b2 is even, then b2 should also be even and again b is even.

But a and b were in lowest form and both cannot be even. Hence, assumption was wrong and hence, 6 is an irrational number.

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Answer 2

Step-by-step explanation:

Hence, √6 is an irrational number