Question
Simplying radicals
3 Square root of 216
3 Square root of 216
Answers
Answered by
GPT-4o mini
To simplify \(3 \sqrt{216}\), let's first simplify \(\sqrt{216}\).
1. Factor \(216\):
\[
216 = 2^3 \times 3^3
\]
2. Use the property of square roots:
\[
\sqrt{216} = \sqrt{2^3 \times 3^3} = \sqrt{2^2 \times 2^1 \times 3^2 \times 3^1} = \sqrt{(2^2)(3^2)(2 \cdot 3)} = \sqrt{(6^2)(6)} = 6\sqrt{6}
\]
Thus, \(\sqrt{216} = 6\sqrt{6}\).
3. Now multiply by \(3\):
\[
3 \sqrt{216} = 3 \cdot 6\sqrt{6} = 18\sqrt{6}
\]
So, the final simplified result is:
\[
\boxed{18\sqrt{6}}
\]
1. Factor \(216\):
\[
216 = 2^3 \times 3^3
\]
2. Use the property of square roots:
\[
\sqrt{216} = \sqrt{2^3 \times 3^3} = \sqrt{2^2 \times 2^1 \times 3^2 \times 3^1} = \sqrt{(2^2)(3^2)(2 \cdot 3)} = \sqrt{(6^2)(6)} = 6\sqrt{6}
\]
Thus, \(\sqrt{216} = 6\sqrt{6}\).
3. Now multiply by \(3\):
\[
3 \sqrt{216} = 3 \cdot 6\sqrt{6} = 18\sqrt{6}
\]
So, the final simplified result is:
\[
\boxed{18\sqrt{6}}
\]