Question

Prove that 2-3√3 is irrational​

Answer 1

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Answer 2

Here is your Answer

Solution

Let , asume that 2-3√3 is rational

Therefore , 2-3√3 = p/q [ where ,p and q are the two integers and co- prime ,where q≠0]

=> 2-3√3 =p/q

=> √3 = p/3q-2

=> √3 = p - 6q/3q

Since, √3 is in the form of a/b .

Therefore, √3 is rational .

But , we know that √3 is irrational .

Therefore, our assumption that 2-3√3 is rational is wrong or false .

Therefore, 2-3√3 is irrational.

Proved .

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