Question

Prove that √3 es irrational.
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Answer 1

Solution:

Let √3 be rational number.

=>√3 = p/q

p/q are integers and have no common factor and q is not equal to 0.

3 = p²/q²

=>3 = p²/q×q

=>3q = p²/q

Case I:

when q = 1

3×1 = p²/1

3 = p²

There is no integer whose square is 3.

So, this case is not possible.

Case II:

When q is not equal to 1.

3q = p²/q

=>Integer is not equal to non integer.

√3 is not a rational number

Thus, it is an irrational number.

Answer 2

Answer:

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