Question
Simplify the product. \[ \sqrt{3} \cdot \sqrt{12} \]
Ask by Curry Bradley. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product simplifies to 6.
Solution
To simplify the product \(\sqrt{3} \cdot \sqrt{12}\), you can use the property of square roots that states:
\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \times b}
\]
Let's apply this property step by step:
1. **Multiply the radicands (the numbers inside the square roots):**
\[
\sqrt{3} \cdot \sqrt{12} = \sqrt{3 \times 12}
\]
2. **Calculate the product inside the square root:**
\[
3 \times 12 = 36
\]
So,
\[
\sqrt{3 \times 12} = \sqrt{36}
\]
3. **Simplify the square root:**
\[
\sqrt{36} = 6
\]
**Therefore,**
\[
\sqrt{3} \cdot \sqrt{12} = 6
\]
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Simplify this solution Beyond the Answer
To simplify the product \(\sqrt{3} \cdot \sqrt{12}\), you can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). First, combine the square roots: \[ \sqrt{3} \cdot \sqrt{12} = \sqrt{3 \cdot 12} = \sqrt{36} \] Next, simplify \(\sqrt{36}\): \[ \sqrt{36} = 6 \] Thus, the simplified product is: \[ \sqrt{3} \cdot \sqrt{12} = 6 \]
