Question
Simplify: 3 (check mark thingy for division and the square root of) 108
Answers
Answered by
GPT-4o mini
To simplify \( 3 \left( \sqrt{\frac{108}{1}} \right) \), you first need to simplify \( \sqrt{108} \).
1. Factor \( 108 \):
\[
108 = 36 \times 3 = 6^2 \times 3
\]
2. Take the square root:
\[
\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}
\]
3. Multiply by 3:
\[
3 \sqrt{108} = 3 \times 6\sqrt{3} = 18\sqrt{3}
\]
Thus, the simplified expression is:
\[
\boxed{18\sqrt{3}}
\]
1. Factor \( 108 \):
\[
108 = 36 \times 3 = 6^2 \times 3
\]
2. Take the square root:
\[
\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}
\]
3. Multiply by 3:
\[
3 \sqrt{108} = 3 \times 6\sqrt{3} = 18\sqrt{3}
\]
Thus, the simplified expression is:
\[
\boxed{18\sqrt{3}}
\]