To determine how many complete pieces can be made from a bridge support beam that is √320 feet long when cut into pieces of √20 feet each, we perform the following calculation:
First, we will simplify the lengths:
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The length of the beam is: \[ \sqrt{320} = \sqrt{64 \times 5} = \sqrt{64} \times \sqrt{5} = 8\sqrt{5} \text{ feet} \]
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The length of each piece is: \[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \text{ feet} \]
Next, we need to find out how many pieces of length \(2\sqrt{5}\) can fit into \(8\sqrt{5}\). We do this by dividing the total length of the beam by the length of each piece:
\[ \frac{8\sqrt{5}}{2\sqrt{5}} = \frac{8}{2} = 4 \]
Thus, the number of complete pieces that can be made is:
\[ \boxed{4} \]