Question

Prove that
$3 + 2 \sqrt{5}$
Is irrational


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Answer 1

Explanation:

refer to the attachment

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Answer 2

Assume that 3+2√5 is rational.

Then,

$= > 3 + 2 \sqrt{5} = \frac{a}{b} \\ = > \sqrt{5} = \frac{a - 3b}{2b}$

This gives that,

$\frac{a - 3b}{2b} \: \: is \: irrational \: but \: \sqrt{5} \: \: is \: an \\ irrational \: number.$

Therefore, the assumption is wrong.

Hence, 3+2√5 is an irrational number.

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