Question

Q-5) Prove that √11 is an irrational number.

Answer 1

Let assume that√11 be a rational number

√11=a/b_____________(where a and b are co prime and their HCF is 1)

√11b=a

Square both side

11b²=a²

a² is a factor of 11

a is also a factor of 11__________(by theorm)

a=11c________________(where c is some integer)

Square both side

a²=22c²

11b²=22c²____________(a² is 11b² proved above)

b²=11c²

b² is a factor of 11

b is also a factor of 11________(by theorm)

Where a and b are factor of 11 and are not co prime

Which contradict our assumption

Hence√11 is irrational number