Simplify

Question:

Simplify: $\frac{2 \sqrt{45}+3 \sqrt{20}}{2 \sqrt{5}}$

 

Solution:

$\frac{2 \sqrt{45}+3 \sqrt{20}}{2 \sqrt{5}}=\frac{2 \sqrt{3 \times 3 \times 5}+3 \sqrt{2 \times 2 \times 5}}{2 \sqrt{5}}$

$=\frac{2 \times 3 \sqrt{5}+3 \times 2 \sqrt{5}}{2 \sqrt{5}}$

$=\frac{6 \sqrt{5}+6 \sqrt{5}}{2 \sqrt{5}}$

$=\frac{12 \sqrt{5}}{2 \sqrt{5}}$

$=6$

Hence, simplified form of $\frac{2 \sqrt{45}+3 \sqrt{20}}{2 \sqrt{5}}$ is 6 .

 

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