Question

prove that 2+3underroot 5 is irrational.

Answer 1

Heya mate, Here is ur answer

Let 2 + √3 be a rational number.

So, 2 + √3 = a/b ( where b≠ 0 )

√3 = a/b -2

But √3 is irrational and a/b-2 is rational.

This contradicts our supposition that 2+√3 is rational number.

So, 2+√3 is an irrational number.

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Answer 2

Hey Cybertronian ＼(^_^)／

$\fbox{By \:using \:the\: contradiction\: method}$

Let
$let \: 2 + 3 \sqrt{5} be \: a \: rational \\ numeral \\ \\ therefore \\ 2 + 3 \sqrt{5} = \frac{x}{y} \\ = > 3 + \sqrt{5} = \frac{x}{y} + 2 \\ \\ now \\ LHS = irrational \: whereas \\ RHS = rational \\ \\ and \: we \: know \: that \: a \: rational \\ numeral \: is \: never \: equivalent \\ to \: an \: irrational \: numeral \\ \\ so \\ 2 + 3 \sqrt{5} is \: an \: irrational \: \\ numerical$

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