Question

Write whether (2 root 45 + 3 root 20 )÷root 20 is rational or irrational

Answer 1

it's a irrational number because root is always a irrational number like
$\sqrt{2 + 5 = \sqrt{7} }$

Answer 2

$The \: \: answer \: \: is \: \: given \: \: below \\ \\ Now, \\ \\ \frac{2 \sqrt{45} + 3 \sqrt{20} }{ \sqrt{20} } \\ \\ = \frac{2 \sqrt{5 \times 3 \times 3} + 3 \sqrt{5 \times 2 \times 2} }{ \sqrt{5 \times 2 \times 2} } \\ \\ = \frac{6 \sqrt{5} + 6 \sqrt{5} }{2 \sqrt{5} } \\ \\ = \frac{12 \sqrt{5} }{2 \sqrt{5} } \\ \\ = 6 \\ \\ and \: \: 6 \: \: is \: \: a \: \: rational \: \: number. \\ \\ Therefore, \: \: the \: \: given \: \: number \\ is \: \: a \: \: rational \: \: number. \\ \\ Thank \: \: you \: \: for \: \: the \: \: question.$