Question

2 root 3 minus 1 is a irrational number prove it

Answer 1

aloha user!!

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$in \: order \: to \: prove \: that \: it \: is \: irrational \\ \: we \: are \: going \: to \: assume \: that \: it \: is \: a \: rational \: number. \\ \:which \: can \: be \: expressed \: in \: the \: form \: \frac{p}{q}. \: so..$

$2 \sqrt{3} - 1 = \frac{p}{q}$
2√3 = P/q + 1
2√3 = P/q + q/q
2√3 = (P + q)/q
√3 = (P + q)/2q

$we \: know \: that \: (P + q)/2q \: is \: rational.$
but √3 is irrational.

these two are not equal.

this is our contradiction to the fact that this number is rational.

so our assumption is wrong 2√3 - 1 is an irrational number.

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hope it helps !!

peace out !!