Question

Prove that(2+root3) is an irrational number

Answer 1

Let us assume (2+√3) is a

rational number.

2+√3 = a/b

[ where a , b are integers and

b≠0 ]

√3 = a/b - 2

=> √3 = (a-2b)/b

Since , a,b are integers . (a-2b)/b is rational ,so, √3 is rational.

But , This contradicts that the √3 is an irrational.

Therefore,

(2+√3) is an irrational number.

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This is the