Question

prove that 4 plus root 3 is an irrational
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Answer 1

Answer:

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Step-by-step explanation:

Let us assume the contrary, that 4−3 is rational.

That is, we can find co-prime a and b (b=0) such that 4−3=ba. 

Therefore 4−ba=3.

Rearranging this equation, we get 3=4−ba

=b4b−a

Since a and b are integers, we get b4b−a is rational, and so 3 is rational.

But this contradicts the fact that 3 is irrational,

This contradicts the fact that 3 is irrational.

This contradiction has arisen because of our incorrect assumption that 4-3 is rational.

so, we conclude that 4−3 is irrational.