Simplify the radical expression.

To simplify the expression \( \sqrt{40} - \sqrt{3} + \sqrt{290} \), we start by simplifying the square roots.

First, simplify \( \sqrt{40} \):
\[
\sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10}
\]

Next, simplify \( \sqrt{290} \):
\[
\sqrt{290} = \sqrt{29 \cdot 10} = \sqrt{29} \cdot \sqrt{10}
\]
Since 29 is a prime number, \( \sqrt{29} \) cannot be simplified further.

Now, substituting these simplifications back into the expression:
\[
\sqrt{40} - \sqrt{3} + \sqrt{290} = 2\sqrt{10} - \sqrt{3} + \sqrt{290}
\]
We can write \( \sqrt{290} \) in terms of \( \sqrt{10} \):
\[
\sqrt{290} = \sqrt{29}\sqrt{10}
\]
So the expression is:
\[
2\sqrt{10} - \sqrt{3} + \sqrt{29}\sqrt{10}
\]

Now combine the \( \sqrt{10} \) parts:
\[
(2 + \sqrt{29})\sqrt{10} - \sqrt{3}
\]

Thus, the simplified form of the expression is:
\[
(2 + \sqrt{29})\sqrt{10} - \sqrt{3}
\]

However, the answers provided do not exactly match our simplified form, showing potential errors in the question or the choices provided.

In conclusion, if I must select based on a simple numerical coefficient for \( \sqrt{10} \), the closest valid option among those provided involves \( 2\sqrt{10} - \sqrt{3} \) though it doesn’t fully incorporate all relevant simplifications:
- The option responds with: \( 8\sqrt{10} - \sqrt{3} \), indicating a clear departure due to arrangements in coefficients or potential out layers not indicated.

None of the choices exactly match our fully simplified expression, but if forced to simplify using \( (2+\sqrt{29})\sqrt{10} - \sqrt{3} \), the closest numerical ratio would be within \( 2\sqrt{10} - \sqrt{3} \).

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