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Prove that root 3 + root 5 is irrational

Answer» HELLO Mate!

let \: x = \sqrt{3} + \sqrt{5} \\ {x}^{<klux>2</klux>} = {( \sqrt{3} + \sqrt{5} )}^{2} \\ {x}^{2} = 3 + 5 + 2 \sqrt{15} \\ \frac{ {x} ^{2} - 8 }{2} = \sqrt{15}

Here, ( x^2 - 8 ) / 2 is rational which is EQUIVALENT to root 15 but we arrise to a contradiction that root 15 is irrational.

That is why !

\sqrt{3} + \sqrt{5} \: is \: irrational

Hope it helps☺!


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