Question

$write \: whether \: 2 \sqrt{45} + 3 \sqrt{20} \div 2 \sqrt{5} \: on \: simplication \: gives \: a \: irrational \: number \: or \: rational \: number$
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Answer 1

Step-by-step explanation:

$2 \sqrt{45} + 3 \sqrt{20} \\ = 2 \times \sqrt{9 \times 5} + 3 \times \sqrt{4 \times 5} \\ = 2 \times \sqrt{9} \times \sqrt{5} + 3 \times \sqrt{4} \times \sqrt{5} \\ = 2 \times 3 \times \sqrt{5 } + 3 \times 2 \times \sqrt{5} \\ = 6 \sqrt{5} + 6 \sqrt{5} \\ = 12 \sqrt{5}$