Question

Show that 2 + root 3

Answer 1

2+√3

2+1.732apx

3.732 ans

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Answer 2

Let us assume to contrary that 2+√3 is rational,

i.e.,

we can find m and n(≠0) two such positive co-prime integers so that,

m/n = 2+√3

m/n - 2 = √3

m - 2n/n = √3

let we say m-2n/m as x

since,

m,n and 2 are integers.

so,

x is also integer.

x is rational.

so, √3 must be rational.

But, this contradicts the fact that √3 is irrational.

This contradiction has arisen due to our incorrect assumption that 2+√3 is rational.

So, we conclude that 2+√3 is irrational