Question

prove that under root 3 + under root 7 is an irrational number

Answer 1

Answer:

Let _/3 + _/7 be rational

Step-by-step explanation:

$\sqrt{3} + \sqrt{7} = \frac{p}{q} \: \: {p \: and \: q \: coprime} \\ \\ square \: both \: sides \\ \\ ( \sqrt{3} + \sqrt{7} ) {}^{2} = ( \frac{p}{q} ) {}^{2} \\ \\ 3 + 7 + 2 \sqrt{21} = \frac{p {}^{2} }{q {}^{2} } \\ 2 \sqrt{21} = \frac{p {}^{2} }{q {}^{2} } - 10 \\ \sqrt{21} =\frac{p {}^{2} }{2q {}^{2} } - 5$

now rhs is rational but lhs is irrational so the no. is irrational