Question
Simplify (10√5)², leaving your answer in exact form.
Answers
GPT-4o mini
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 \(\boxed{500}\).
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 \(\boxed{500}\).