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

Sept. 17, 2019

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Archangel Macsika

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

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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