Question

27. Prove that root2+root3 is an irrational number​

Answer 1

Solution:

Let us suppose that √2+√3 is rational.

Let √2+√3=,

where a,b are integers and b≠0

Therefore,

On Squaring both sides , we get

Rearranging the terms ,

Since , a,b are integers ,

is rational, and so √3 is rational.

This contradicts the fact √3 is irrational.

Hence, √2+√3 is irrational.

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