Evaluate the following radical expression:

$\sqrt{72}+\sqrt{20}-\sqrt{18}$

The correct answer is $3\sqrt{2}+2\sqrt{5}$.

To evaluate the radical expression, we simplify each square root term individually by factoring out perfect squares, and then combine the like radical terms.
Given expression:

$\sqrt{72}+\sqrt{20}-\sqrt{18}$

Step 1: Simplify each radical term into its simplest form.
Identify the largest perfect square factor for each number under the radical:
1. Simplify $\sqrt{72}$:
Since $72=36\times 2$, and $36$ is a perfect square ($6^2=36$):

$\sqrt{72}=\sqrt{36\times 2}=\sqrt{36}\times \sqrt{2}=6\sqrt{2}$

2. Simplify $\sqrt{20}$:
Since $20=4\times 5$, and $4$ is a perfect square ($2^2=4$):

$\sqrt{20}=\sqrt{4\times 5}=\sqrt{4}\times \sqrt{5}=2\sqrt{5}$

3. Simplify $\sqrt{18}$:
Since $18=9\times 2$, and $9$ is a perfect square ($3^2=9$):

$\sqrt{18}=\sqrt{9\times 2}=\sqrt{9}\times \sqrt{2}=3\sqrt{2}$

Step 2: Substitute the simplified expressions back into the main expression.

$\sqrt{72}+\sqrt{20}-\sqrt{18}=6\sqrt{2}+2\sqrt{5}-3\sqrt{2}$

Step 3: Combine like terms.
Group and subtract the terms containing $\sqrt{2}$:

$(6\sqrt{2}-3\sqrt{2})+2\sqrt{5}=3\sqrt{2}+2\sqrt{5}$

Thus, the final simplified expression is $3\sqrt{2}+2\sqrt{5}$.