Question
Simplify. \( \left(-\frac{1}{2} \sqrt{2}\right)(-6 \sqrt{18}) \)
Ask by Burton Todd. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified result is 18.
Solution
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{-1}{2}\right)\sqrt{2}\times \left(-6\right)\sqrt{18}\)
- step1: Rewrite the fraction:
\(\left(-\frac{1}{2}\right)\sqrt{2}\times \left(-6\right)\sqrt{18}\)
- step2: Remove the parentheses:
\(-\frac{1}{2}\sqrt{2}\times \left(-6\right)\sqrt{18}\)
- step3: Simplify the root:
\(-\frac{1}{2}\sqrt{2}\times \left(-6\right)\times 3\sqrt{2}\)
- step4: Rewrite the expression:
\(\frac{1}{2}\sqrt{2}\times 6\times 3\sqrt{2}\)
- step5: Multiply the terms:
\(9\sqrt{2}\times \sqrt{2}\)
- step6: Multiply the terms:
\(9\times 2\)
- step7: Multiply the numbers:
\(18\)
To simplify the expression \( \left(-\frac{1}{2} \sqrt{2}\right)(-6 \sqrt{18}) \), we can follow these steps:
1. **Multiply the constants**:
\[
-\frac{1}{2} \times -6 = 3
\]
2. **Multiply the square roots**:
\[
\sqrt{2} \times \sqrt{18} = \sqrt{2 \times 18} = \sqrt{36} = 6
\]
3. **Combine the results**:
\[
3 \times 6 = 18
\]
Thus, the simplified result is \( 18 \).
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Mind Expander
To simplify \( \left(-\frac{1}{2} \sqrt{2}\right)(-6 \sqrt{18}) \), we start by multiplying the two parts together. First, notice that the negative signs cancel out: \[ \left(-\frac{1}{2}\right)(-6) = \frac{1}{2} \times 6 = 3. \] Next, simplify \( \sqrt{18} \): \[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}. \] Now, substitute back into our expression: \[ 3 \times \sqrt{2} \times 3\sqrt{2} = 3 \times 3 \times \sqrt{2} \times \sqrt{2} = 9 \times 2 = 18. \] So, the final simplified result is: \[ \boxed{18}. \]