Question

Show that root n is an irrational number if n is not a perfect square​

Answer 1

Answer:

√n is irrational if n is not a perfect square

Step-by-step explanation:

if n is not a perfect square then √n is irrational.

let on the contrary say it is rational

Then

√n=p/q (q is not equal to 0 where p nd q are coprime integers).

so n=p²/q²

p²=nq²

this shows p divides q.

which is a contradiction.

hence √n is irrational if n is not a perfect square.

I hope it helps you.

Answer 2

If n is not a perfect square then is irrational

Let on the contrary say it is rational .

Then

where p and q are coprime integers.

so n =p2/q2

p2 =nq2

This shows p divides q

which is a contradiction.

Hence is irrational if n is not a perfect square.

HOPE IT HELPS YOU...