Question

prove that root 3 is an irrational number

Answer 1

He bro root2 ko change krke root3 rakh do na

Answer 2

Let us assume that root 3 is rational,

So root 3=a/b (where a and b are Co prime and have 1 as Hcf)

Squaring both sides,

3 = a2/b2

3b2=a2....(1)

a2/3=b2

So, a2 is divisible by 3 and so, a I also divisible by 3(by theorem)

Now,

a=3c

Squaring both sides,

a2=9c2

3b2=9c2(from eq. 1)

b2=3c2

b2/3=c2

so, b2 is divisible by 3 and hence b is also divisible by 3 (by theorem)

Now, we can conclude that a and b are divisible by 3 and 1 both... So they are not Co prime numbers.

Hence our assumption was wrong

Therefore, root 3 is irrational...

Hence proved

Hope it helps you dear.....