Question
Multiply. Write your answer in simplest form. \( \sqrt{10} \cdot \sqrt{5} \)
Ask by Love Wade. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 5\sqrt{2} \)
Solution
To multiply \( \sqrt{10} \) and \( \sqrt{5} \) and express the result in its simplest form, follow these steps:
1. **Multiply the Radicands:**
\[
\sqrt{10} \cdot \sqrt{5} = \sqrt{10 \times 5} = \sqrt{50}
\]
2. **Simplify the Square Root:**
\[
\sqrt{50} = \sqrt{25 \times 2}
\]
Since \( 25 \) is a perfect square (\( 5^2 = 25 \)), you can simplify further:
\[
\sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
\]
3. **Final Answer:**
\[
\sqrt{10} \cdot \sqrt{5} = 5\sqrt{2}
\]
**So, the simplest form of \( \sqrt{10} \cdot \sqrt{5} \) is \( 5\sqrt{2} \).**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
When you multiply square roots, you can combine them under a single square root. So, \( \sqrt{10} \cdot \sqrt{5} = \sqrt{10 \cdot 5} = \sqrt{50} \). To simplify \( \sqrt{50} \), we can factor it into \( \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \). Therefore, your final answer is \( 5\sqrt{2} \). Embrace the beauty of square roots! They often pop up in various fields, from architecture to physics. Understanding how to manipulate them not only helps in solving equations but also in real-world situations, like optimizing areas or calculating distances. Next time you're measuring an irregular space, remember that \( \sqrt{50} \) might just be the key to a neat calculation!
