1.

Prove that (5 – 2√3) is an irrational number.

Answer»

Let us assume that (5 – 2√3) is a rational.

Subtract given number form 5, considering 5 is a rational number.

As we know, Difference of two rational numbers is a rational.

5 – (5 – 2√3) is rational

2√3 is rational

Which is only possible if 2 is rational and √3 is rational

As we know, product of two rational number is rational.

But the fact is √3 is an irrational.

Which is contradict to our assumption.

(5 – 2√3) is an irrational number.



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