Question

prove root 2 + root 3 is irrational..​

Answer 1

1st solution

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

Let √2+√3=a/b

where a,b are integers and b≠0

Therefore,

√2 =a/b-√3

On Squaring both sides , we get

2=\frac{a^{2}}{b^{2}}+3-2\times\frac{a}{b}\times\sqrt{3}2

Rearranging the terms ,

\frac{2a}{b}\times\sqrt{3}=\frac{a^{2}}{b^{2}}+3-2

a²/b²=1

√3=a²+b²/2ab

by this way √2+√3 is irrational

2nd solution

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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