Question

prove that root 2 + root 3 is an irrational number

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Answer 1

Step-by-step explanation:

Solution:

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

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0Therefore,

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0Therefore,On Squaring both sides , we get

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0Therefore,On Squaring both sides , we getRearranging the terms ,

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0Therefore,On Squaring both sides , we getRearranging the terms ,Since , a,b are integers ,

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0Therefore,On Squaring both sides , we getRearranging the terms ,Since , a,b are integers , is rational, and so √3 is rational.

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0Therefore,On Squaring both sides , we getRearranging the terms ,Since , a,b are integers , is rational, and so √3 is rational.This contradicts the fact √3 is irrational.

Solution:Let us suppose that √2+√3 is rational.Let √2+√3=,where a,b are integers and b≠0Therefore,On Squaring both sides , we getRearranging 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