Question

Prove that yn is not a rational number, if nis not a perfect square.​

Answer 1

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Answer 2

If n is not a perfect square then √n is irrational

Let on the contrary say it is rational.

Then,

√n-q0 where p and q are coprime

q

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.