Question

if p is prime number, show that root p is irrational!!!​

Answer 1

Answer:

$\sqrt{p}$ is an irrational number

Step-by-step explanation:

I'm going to use contradiction.

Let $\sqrt{p}$ is a rational number $\frac{b}{a}$.

Then, $(\sqrt{p})^2=(\frac{b}{a} )^2$ ⇒ $p=\frac{b^2}{a^2}$ ⇒ ∴ $a^2p=b^2$

Hence, b² divides p. ⇒ ∴ b divides p ⇒ We can let $p=bk$.

This is contradiction. p is a prime number.

So $\sqrt{p}$ is an irrational!