Question
Multiply. Write your answer in simplest form. \( \sqrt{30} \cdot \sqrt{5} \)
Ask by Joseph Perkins. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(5\sqrt{6}\)
Solution
To multiply \(\sqrt{30}\) and \(\sqrt{5}\) and simplify the expression, follow these steps:
1. **Multiply the Square Roots:**
\[
\sqrt{30} \cdot \sqrt{5} = \sqrt{30 \times 5} = \sqrt{150}
\]
2. **Simplify \(\sqrt{150}\):**
Break down 150 into its prime factors to find perfect squares:
\[
150 = 25 \times 6
\]
Here, 25 is a perfect square because \(25 = 5^2\).
3. **Apply the Square Root to the Factors:**
\[
\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}
\]
So, the simplified form of \(\sqrt{30} \cdot \sqrt{5}\) is:
\[
5\sqrt{6}
\]
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Simplify this solution The Deep Dive
When you multiply square roots, you can multiply the numbers inside the radicals together. So, \( \sqrt{30} \cdot \sqrt{5} = \sqrt{30 \cdot 5} = \sqrt{150} \). Now, to simplify \( \sqrt{150} \), we can break it down into its prime factors: \( 150 = 25 \cdot 6 = 5^2 \cdot 6 \). Thus, \( \sqrt{150} = \sqrt{25} \cdot \sqrt{6} = 5\sqrt{6} \). So the answer in simplest form is \( 5\sqrt{6} \).
