Question

prove that, 5-2root 3 is irrational

Answer 1

Solution:

Let us assume 5-2√3 is

rational.

5-2√3 = a/b [ where a,b are integers and b ≠ 0 ]

=> 2√3 = 5-a/b

=> 2√3 = (5b-a)/b

=> √3 = (5b-a)/2b

Since , a,b are integers ,

(5b-a)/2b is rational ,so √3 is

rational.

But , this contradicts that the

√3 is irrational.

Therefore.

5-2√3 is rational.

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