Simplify (10√5)², leaving your answer in exact form.

Answer 1

To simplify \((10\sqrt{5})^2\), you can follow these steps:

1. Square the coefficient (10): \[ 10^2 = 100 \]

2. Square the radical (\(\sqrt{5}\)): \[ (\sqrt{5})^2 = 5 \]

3. Combine the results: \[ (10\sqrt{5})^2 = 10^2 \cdot (\sqrt{5})^2 = 100 \cdot 5 = 500 \]

Thus, the simplified form of \((10\sqrt{5})^2\) is \(\boxed{500}\).