Question

Prove that V3 is an irrational number.​

Answer 1

Step-by-step explanation:

Say 3–√ is rational. Then 3–√ can be represented as ab, where a and b have no common factors.

So 3=a2b2 and 3b2=a2. Now a2 must be divisible by 3, but then so must a (fundamental theorem of arithmetic). So we have 3b2=(3k)2 and 3b2=9k2 or even b2=3k2 and now we have a contradiction.

Answer 2

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