Question:
Write whether $\frac{2 \sqrt{45}+3 \sqrt{20}}{2 \sqrt{5}}$ on simplification gives a rational or an irrational number.
Solution:
Let us simplify $\frac{2 \sqrt{45}+3 \sqrt{20}}{2 \sqrt{5}}$
$\frac{2 \sqrt{45}+3 \sqrt{20}}{2 \sqrt{5}}=\frac{6 \sqrt{5}+6 \sqrt{5}}{2 \sqrt{5}}$
$=\frac{12 \sqrt{5}}{2 \sqrt{5}}$
=6
6 is rational number
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