# Prove that if x^3 is irrational, then x is irrational

## Solution Using Proof by Contradiction

Let p: be "x^{3} is irrational" and q be "x is irrational"

we can assume that p implies ¬q is true, when p is true and ¬q is true

Interpreting this, "x^{3} is irrational" and "x is not irrational"

Now, if "x is not irrational" is true, then "x is rational" will also be true

Using proof by contradiction to show that x^{3} is irrational by proving that x is rational

let x = a∕b, where a is a set of all real numbers and b ≠ 0

Since, we've shown that x is rational

∴ x^{3} = a^{3}∕b^{3}

x^{3}b^{3} =a^{3}

x * x * x * b * b * b = a * a * a