Write whether

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

is rational number

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