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  • Given that   is an irrational number, prove that <img alt="(2+\sqrt 3 )" src="https://entrancecorner.codecogs.com/gif.latex?%282&plus;%5Csqrt%203%20%29"

Given that \sqrt 3  is an irrational number, prove that (2+\sqrt 3 ) is an irrational number

 

 

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Let (2+\sqrt 3 ) is a rational number 

2 + \sqrt 3 = a/b \\\\ \sqrt 3 = a/b -2 \\\\ \sqrt 3 \neq \frac{a-2b}{b}

Here \sqrt 3 is an irrational number so our assumption is wrong hence (2+\sqrt 3 ) is an irrational number 

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