Question

Prove that root p is irrational​

Answer 1

$\huge\underline\mathfrak{Question-}$

Prove that √p is irrational.

$\huge\underline\mathfrak{Answer-}$

To prove ;- √p is irrational.

Assuming √p a rational number.

So , p = a / b { Here a & b are composite }

=> a = pb

=> a² = p²b²

Here ,
If a² gets divisible by p² then it follows that it is also divisible by p or we can also write as ;-

=> b² = p²c²

Than ,
If b² is divisible by p² then it follows that b is also b is also divisible by f.

So ,
We could observe that here a & b both have p as common factor but a & b are composite numbers.

Thus , we can say that √p is irrational.