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## Homework Statement

Prove that if x^2 is irrational then x must be irrational.

## Homework Equations

## The Attempt at a Solution

Maybe do proof by contradiction. I'm not really sure where to start.

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- Thread starter kmeado07
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Prove that if x^2 is irrational then x must be irrational.

Maybe do proof by contradiction. I'm not really sure where to start.

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Office_Shredder

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Proof by contradiction sounds good. What if x is rational?

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HallsofIvy

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"Suppose x is rational. Then x= __________"

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so i let x= a/b

then obviously x^2 = a^2/b^2

im not sure how to continue to reach the contradiction

then obviously x^2 = a^2/b^2

im not sure how to continue to reach the contradiction

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Dick

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HallsofIvy

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so i let x= a/b

then obviously x^2 = a^2/b^2

im not sure how to continue to reach the contradiction

It is not enough just to say "let x= a/b" without saying what a and b are. A number is rational if and only if it can be expressed as a ratio of

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