nth-root of irrational will always give irrational numbers?

Mohammad Cannon

Mohammad Cannon

Answered question

2022-06-19

nth-root of irrational will always give irrational numbers?

Answer & Explanation

Alisa Gilmore

Alisa Gilmore

Beginner2022-06-20Added 22 answers

Obviously, if p is rational, then p 2 must also be rational.
p Q p 2 Q .
Take the contraposition, we see that if x is irrational, then x must also be irrational.
p 2 Q p Q .
By negative power I assume you mean ( 1 / n)-th power (it is obvious that ( 2 ) 2 = 1 2 Q . It is true by the statement above — just replace 2 by n .

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