Question

17. Prove that 5+372 is an irrational number.​

Answer 1

Answer:

$t.p = 5 + 3 \sqrt{2} \: is \: an \: irrational \: number \\proof = \\ let \: 5 + 3 \sqrt{2} is \: rational \: number \\ so \: 5 + 3 \sqrt{2} = \frac{p}{q} (p \: and \: q \: are \: real \: no. \: and \: q \: not \: equal \: to \: 0) \\ \: \: 3 \sqrt{2} = \frac{p}{q} - 5 \\ 3\sqrt{2} = \frac{p - 5q}{q} \\ \sqrt{2} = \frac{p - 5q}{3q} \\ \: \: \: \: \: \: \: in \: r.h.s \: \frac{p - 5q}{3q} is \: a \: rational \: number \\ but \: in \: l.h.s \: \sqrt{2} \: is \: irrational \: number \\ this \: is \: not \: possible \: as \: a \: number \: may \: be \: rational \: or \: irrational \: \\ and \: irrational \: is \: not \: equal \: to \: rational \: number. \\ this \: contradicts \: our \: assumption. \\ therefore \: 5 + 3 \sqrt{2} is \: an \: irrational \: number. \\ \\ \\ hope \: it \: helps.............. \\ plz \: mark \: as \: brainliest..............$