Question

show that
$2 - \sqrt{3}$
is an irrational number​

Answer 1

Solution :

Let us assume ( 2 - √3 ) is

a rational number.

2 - √3 = a/b

[ a, b are integers and b≠0 ]

=> √3 = 2 - a/b

=> √3 = ( 2b - a )/b

Since ,

a, b are integers , (2b-a)/b is

rational number , so, √3 is

also rational.And we know

that √3 is an irrational number.

But , this is a contradiction to

our assumption .

So, we conclude that 2-√3

is an irrational number.

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Answer 2

hope my answer help you