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Prove that 2 + 5\sqrt3 is an irrational number, given that \sqrt3  is an irrational number.

 

 

Answers (1)

Let 2 + 5\sqrt3 = a

where 'a' is a rational number.

\Rightarrow \sqrt 3 = \frac{a-2}{5}

[Given in the question that \sqrt 3 is an irrational number]

Which is a contradiction as LHS is irrational and RHS is rational.

So, 2 + 5\sqrt3 can not be rational

hence, proved, 2 + 5\sqrt3 is irrational.

Posted by

Safeer PP

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