Question

prove that root 11 is irrational....​

Answer 1

Let as assume that √11 is a rational number.

A rational number can be written in the form of p/q where q ≠ 0 and p , q are non negative number.

√11 = p/q ....( Where p and q are co prime number )

Squaring both side !

11 = p²/q²

11 q² = p² ......( i )

p² is divisible by 11

p will also divisible by 11

Let p = 11 m ( Where m is any positive integer )

Squaring both side

p² = 121m²

Putting in ( i )

11 q² = 121m²

q² = 11 m²

q² is divisible by 11

q will also divisible by 11

Since p and q both are divisible by same number 11

So, they are not co - prime .

Hence Our assumption is Wrong √11 is an irrational number .