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

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

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

If you would like to see a different solution or have a question or concern Kindly let us know