Question
What is this expression in simplified form? \[ \begin{array}{l}3 \sqrt{3} \cdot 6 \sqrt{6} \\ \text { A. } 54 \sqrt{2} \\ \text { B. } 18 \sqrt{2} \\ \text { O C. } 18 \sqrt{3} \\ \text { D. } 54\end{array} \]
Ask by Campbell Mckenzie. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is \(54\sqrt{2}\).
Solution
First, multiply the constants:
\[
3 \times 6 = 18.
\]
Next, multiply the radicals:
\[
\sqrt{3} \times \sqrt{6} = \sqrt{18}.
\]
Simplify \(\sqrt{18}\) by recognizing that \(18 = 9 \times 2\):
\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}.
\]
Now multiply the constant and radical parts:
\[
18 \times 3\sqrt{2} = 54\sqrt{2}.
\]
Thus, the simplified expression is \(\boxed{54\sqrt{2}}\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To simplify the expression \( 3 \sqrt{3} \cdot 6 \sqrt{6} \), we start by multiplying the coefficients and the square roots separately: 1. **Coefficients:** Multiply \( 3 \cdot 6 = 18 \). 2. **Square Roots:** Multiply \( \sqrt{3} \cdot \sqrt{6} = \sqrt{18} \). 3. **Now substitute \( \sqrt{18} \):** We know that \( \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3 \sqrt{2} \). So when we combine everything together: \[ 3 \sqrt{3} \cdot 6 \sqrt{6} = 18 \cdot 3 \sqrt{2} = 54 \sqrt{2} \]. Thus, the simplified form is \( \boxed{54 \sqrt{2}} \), which corresponds to option A.
