Question

Prove that root 3 is an irrational number...

Answer 1

Answer:

The answer of root 3 is 1.73205080756888 as it is non terminating and non repeating/ recurring.

Answer 2

Answer:

assume that √3 is rational

√3=a/b

square on both sides

3=a^2/b^2

3b^2=a^2

therefore 3 divides a^2 and a

put a=3c

3b^2=(3c)^2

3b^2=9c^2

b^2=3c^2

therefore, 3divides b^2 and b

therefore 3 is the common factor of a and b

but we assume that 1 is the common factor of a and b

by contradiction

√3 is irrational....

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