Question

prove that under root 3 is irrational number
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Answer 1

Let us assume that root 3 is rational.

Root 3 = a/b where a and b are integers and coprimes.

Root 3 * b = a

Square LHS and RHS

3b2 = a2

b2 = a2/3

Therefore 3 divides a2 and 3 divides a.

Now take ,

a = 3c

Square ,

a2 = 9c2

3b2 = 9c2

b2/3 = c2

Therefore 3 divides b2 and b.

which is not possible

hence our assumption is wrong root 3 is irrational

Answer 2

It is irrational and proof is given below