Solution to Prove that if x^3 is irrational, then x is irrational - Sikademy
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Prove that if x^3 is irrational, then x is irrational

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Solution Using Proof by Contradiction

Let p: be "x3 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, "x3 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 x3 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
∴ x3 = a3∕b3
x3b3 =a3
x * x * x * b * b * b = a * a * a

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