Question

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

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

Gives a rational number