We need to find the sum of two square roots, $\sqrt{3}$ and $5\sqrt{10}$, and express it in its simplest form.

$\text{Sum} = \sqrt{3} + 5\sqrt{10}$

There are no like terms between $\sqrt{3}$ and $5\sqrt{10}$, so the expression is already in its simplest form. Therefore, the sum is:

$\sqrt{3} + 5\sqrt{10}$

This is the final answer.

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Here are 5 related questions for further practice:

1. Simplify $2\sqrt{5} + 3\sqrt{5}$.
2. Find the sum of $\sqrt{2}$ and $4\sqrt{8}$.
3. Simplify $7\sqrt{6} - 3\sqrt{6}$.
4. Add $2\sqrt{7} + \sqrt{28}$ and simplify.
5. Calculate $\sqrt{12} + \sqrt{27}$ and simplify.

Tip: When adding or subtracting square roots, you can only combine terms with the same radical (i.e., the same number inside the square root).