Question

Prove that if x^3 is irrational and x >=0 then the square root of x is irrational.

Answer 1

The number $x$ is irrational since $c$ and $c^{1/3}$ are irrational.

An irrational number that cannot be represented by rational numbers, which comprises all integers and many non-integers.

Let be $c$ an irrational number so that $c = x^{3}$ and $x \ge 0$. By Algebra we know that $c^{1/3} \ge 0$ and we can rearrange the formula by means of the following expression:

$c^{1/3} = x$ (1)

If $c$ is an irrational number and the cubic root is a form of irrational number, then then $x$ must be irrational.

We kindly invite to check this question on irrational numbers: https://brainly.com/question/528650