Question

write whether
$\frac{2 \sqrt{45 } + 3 \sqrt{20} }{ 2 \sqrt{5} }$
gives rational no. or irrational no.

Answer 1

here is the answer

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Answer 2

GOOD NIGHT

$2 \sqrt{45} + 3 \sqrt{20} \\ - - - - - - \\ \: \: \: \: \: 2 \sqrt{5} \\ \\ 2 \sqrt{3 {}^{2} \times 5} + 3 \sqrt{2 {}^{2} \times 5} \\ - - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: 2 \sqrt{5} \\ \\ 6 \sqrt{5} + 6 \sqrt{5} \\ - - - - - \\ \: \: \: \: \: \: 2 \sqrt{5} \\ \\ 12 \sqrt{5} \\ - - - \\ 2 \sqrt{5} \\ \\ \\ = 6 \\ \\ 6 \: can \:be \: written \: as \: in \: the \: form \: \\ of \: p \div q \: \: i \: e \: 6 \div 1 \\ \\ so \: it \: is \: rational \: number \:$