Question

Prove the following are irrational
a) 3+ √ 7

Answer 1

Answer:

Here,

Root 7 is an irrational number.

So,

the whole is an irrational number.

Answer 2

To Prove :

$3 + \sqrt{7} \: as \: an \: irrational \: number$

Solution :

$let \: \: 3 + \sqrt{7} \: is \: a \: rational \: number \\ so \: \: 3 + \sqrt{7} = \frac{p}{q} (where \: p \: and \: q \: are \: co - prime \: and \: q \: is \: not \: equal \: to \: 0 \\ \sqrt{7} = \frac{p}{q} - 3 \\ \sqrt{7} = \frac{p - 3q}{q}$

$here \: \sqrt{7} \: is \: irrational \: while \: \frac{p - 3q}{q} \: is \: rational \\ so \: our \: assumption \: that \: 3 + \sqrt{7} \: is \: rational \: number \: is \: wrong\\ so \: 3 + \sqrt{7} \: is \: an \: irrational \: number$

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