Question
Multiply. Write your answer in simplest form. \( \sqrt{2} \cdot \sqrt{15} \)
Ask by Rodriguez Black. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product of \( \sqrt{2} \) and \( \sqrt{15} \) is \( \sqrt{30} \).
Solution
To multiply \( \sqrt{2} \) and \( \sqrt{15} \) and simplify the expression, follow these steps:
1. **Multiply the Radicands:**
\[
\sqrt{2} \cdot \sqrt{15} = \sqrt{2 \times 15}
\]
2. **Calculate the Product Inside the Square Root:**
\[
\sqrt{2 \times 15} = \sqrt{30}
\]
3. **Simplify the Square Root (if possible):**
- **Prime Factorization of 30:**
\[
30 = 2 \times 3 \times 5
\]
- Since there are no repeated prime factors, \( \sqrt{30} \) cannot be simplified further.
**Final Answer:**
\[
\sqrt{30}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To multiply the square roots, you can use the property \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \). In this case: \[ \sqrt{2} \cdot \sqrt{15} = \sqrt{2 \cdot 15} = \sqrt{30} \] Since 30 does not have any perfect square factors (other than 1), \( \sqrt{30} \) is already in its simplest form. Therefore, the answer is: \[ \sqrt{30} \]
