Question

Prove that √6 is an irrational number.

Answer 1

Prove that √6 is an irrational number.

But a and b were in lowest form and both cannot be even. Hence assumption was wrong and hence√6 is an irrational number. NOTE: √6=ab , this representation is in lowest terms and hence, a and b have no common factors.So it is an irrational number.

Hope it helps ✔️

Answer 2

Answer:

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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.