Prove that<img wi

Given:

To prove:
is irrational.

Proof:

Let assume that is rational

Therefore it can be expressed in the form of , where p and q are integers and q≠0

Therefore we can write,

Squaring both sides we get,

Apply the formula ( a - b )2 = a+ b2 - 2ab in ,

is a rational number as p and q are integers.

This contradicts the fact that √3 is irrational, so our assumption is incorrect.

Therefore is irrational.

Note: Sometimes when something needs to be proved, prove it by contradiction.
Where you are asked to prove that a number is irrational prove it by assuming that it is rational number

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