To simplify the expression \(4\sqrt{45} + 3\sqrt{245}\), we first simplify each radical individually.
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Simplifying \( \sqrt{45} \):
\[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \]
Therefore: \[ 4\sqrt{45} = 4 \cdot 3\sqrt{5} = 12\sqrt{5} \]
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Simplifying \( \sqrt{245} \):
\[ \sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \cdot \sqrt{5} = 7\sqrt{5} \]
Therefore: \[ 3\sqrt{245} = 3 \cdot 7\sqrt{5} = 21\sqrt{5} \]
Now, we can combine the two terms:
\[ 4\sqrt{45} + 3\sqrt{245} = 12\sqrt{5} + 21\sqrt{5} = (12 + 21)\sqrt{5} = 33\sqrt{5} \]
Thus, the final result is:
\[ \boxed{33\sqrt{5}} \]