Question

Prove that 5-2√3is an irrational number

Answer 1

2√3 is a irrational number

and 5 is a rational number

so Rational -Irrationnal = Irrationnal

Answer 2

Solution:

Let us assume given number

(5-2√3 ) is rational.

5-2√3 = a/b

where a,b are integers, and

b≠0

=> -2√3 = a/b - 5

=> -2√3 = (a-5b)/b

=> √3 = (a-5b)/(-2b)

=> √3 = (5b-a)/2b

Since , a,b are integers ,

(5b-a)/2b is a rational number,so, √3 is rational.

But , It contradicts the fact that

√3 is an irrational.

Therefore,

5-2√3 is an irrational.

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