Question

Prove of underroot n is an irrational number

Answer 1

HOPE THIS HELPS YOU..

Answer 2

Answer:

Let √n is a rational number,

Then, by the property of rational number,

√n = p/q

Where, p and q are distinct integers such that q ≠ 0,

By squaring,

n = p²/q²

⇒ q²n = p² -----(1)

⇒ p² is a multiple of n

⇒ p is a multiple of n.

So we can write,

p = an

Where a is any number,

From equation (1),

q²n = a²n² ⇒ q² = a² n

⇒ q is a multiple of n,

⇒ p and q are not distinct,

Which is a contradiction,

Thus, our assumption is wrong,

Hence, √n is not a rational number,

⇒ √n is an irrational number

Hence, proved.....