Math, asked by neha1418, 10 months ago

prove that 3 + 2 root 5 is irrational

Answers

Answered by Anonymous

Step-by-step explanation:

$to \: prove \: that$

$3 + 2 \sqrt{5 } \: is \: a \: irrational \: number$

$\: let \: us \: assume \: that \: 3 + 2 \sqrt{5} \: is \: a \: rational \: number \:$

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

$so \: b \: = 0$

$a \: and \: b \: are \: co \: prime \: number$

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

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

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

$wkt$

$\sqrt{5} \: is \: a \: irrational \: number$

$hence \: 3 + 2 \sqrt{5} \: is \: a \: irrational \: number$

$\frac{a - 3b}{2b } \: is \: a \: rational \: number$

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