Prove that 5 – √3 is irrational. – InterviewSolution

InterviewSolution

1.

Prove that 5 – √3 is irrational.

Answer»

Let 5 – √3 is a rational number.

we have to find out two integers a and b such as

5 - √3 = a/b

- √3 = a/b - 5

√3 = 5 - a/b

√3 = (5b - a)/b

a, b and 5 all are integers

(5b - a)/b is a rational number.

√3 will be also rational number.

But this contradicts the fact that √3 is an irrational number.

So our hypothesis is wrong.

Hence, 5 – √3 is an irrational number.

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