Question
4) \( \sqrt{6} \times 2 \sqrt{3} \)
Ask by Pierce Medina. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 6\sqrt{2} \)
Solution
To simplify the expression \( \sqrt{6} \times 2 \sqrt{3} \), follow these steps:
1. **Rearrange the Terms:**
You can rearrange the constants and the square roots to make the multiplication clearer:
\[
\sqrt{6} \times 2 \sqrt{3} = 2 \times \sqrt{6} \times \sqrt{3}
\]
2. **Multiply the Square Roots:**
Use the property of square roots that \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\):
\[
\sqrt{6} \times \sqrt{3} = \sqrt{6 \times 3} = \sqrt{18}
\]
3. **Simplify \(\sqrt{18}\):**
Factor 18 into a product of a perfect square and another factor:
\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
\]
4. **Combine All Parts:**
Multiply the constant outside the square root by the simplified square root:
\[
2 \times 3\sqrt{2} = 6\sqrt{2}
\]
**Final Answer:**
\[
\sqrt{6} \times 2 \sqrt{3} = 6\sqrt{2}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
First, let's simplify the expression \( \sqrt{6} \times 2 \sqrt{3} \). We can rearrange it as \( 2(\sqrt{6} \times \sqrt{3}) \). Using the property of square roots that \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \), we have \( \sqrt{6 \times 3} = \sqrt{18} \). Therefore, the expression simplifies to \( 2\sqrt{18} \). Since \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \), we finally have \( 2 \times 3\sqrt{2} = 6\sqrt{2} \). Thus, the answer is \( 6\sqrt{2} \).
