Question

maths
prove that
$\sqrt{11 }$
is irrational number​

Answer 1

Yes, √11 is a irrational number

Answer 2

let √11 be rational number

√11 = p/q (where p and q are integers and q is not equal to zero)

Squaring Both sides

(√11)² = (p/q)²

11 = p²/q²

11q² = p²

here

we see that,

11 divide p

and

11 also divide p² .....(¡)

Let p be 11

11q² = (11)²

11q² = 121

q² = 11

here,

11 divide q

and

11 also divide q² ....(¡¡)

from (¡) and (¡¡) we get,

11 is a common factor of p and q.

so,

our assumption is wrong

and

Hence,

√11 is a irrational number.