Question

35.
Prove that root
3 is an irrational number.​

Answer 1

Answer:

answer to the given ques

Answer 2

Answer:

Let us assume that  $\sqrt{3}$ is rational.

$\sqrt{3}$  = a/b where a and b are integers and coprimes.

$\sqrt{3}$  b = a

Square LHS and RHS

3b² = a²

Therefore 3 is a factor of  a² and 3 is also a factor of a.

Now take ,

a = 3c

Square ,

a² = 9c²

3b² = 9c²

b²/3 = c²

Therefore 3 is a factor of b² and 3 is also a factor of b.

∴3 is a factor of both a & b

So $\sqrt{3}$ is irrational.

                        Hope it helps you^_^