Question
Multiply. Write your answer in simplest form. \( \sqrt{40} \cdot \sqrt{11} \)
Ask by Turner Fuentes. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2\sqrt{110} \)
Solution
To multiply \( \sqrt{40} \) and \( \sqrt{11} \) and express the result in its simplest form, follow these steps:
1. **Use the Property of Square Roots**:
\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \times b}
\]
Applying this property:
\[
\sqrt{40} \cdot \sqrt{11} = \sqrt{40 \times 11} = \sqrt{440}
\]
2. **Simplify \( \sqrt{440} \)**:
Factorize 440 to find any perfect squares:
\[
440 = 4 \times 110
\]
Since 4 is a perfect square (\( 2^2 \)):
\[
\sqrt{440} = \sqrt{4 \times 110} = \sqrt{4} \times \sqrt{110} = 2 \times \sqrt{110}
\]
3. **Final Answer**:
The expression \( \sqrt{40} \cdot \sqrt{11} \) simplified is:
\[
2\sqrt{110}
\]
**Answer:** \( 2\sqrt{110} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To multiply these square roots, we can use the property that \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \). So, \( \sqrt{40} \cdot \sqrt{11} = \sqrt{40 \cdot 11} = \sqrt{440} \). Now, let's simplify \( \sqrt{440} \). First, we can factor \( 440 \) into its prime factors: \( 440 = 4 \cdot 110 = 4 \cdot 10 \cdot 11 = 2^2 \cdot 2 \cdot 5 \cdot 11 \). Since \( \sqrt{4} = 2 \), we have \( \sqrt{440} = \sqrt{4 \cdot 110} = 2\sqrt{110} \). Thus, the final answer is \( 2\sqrt{110} \).
