Question
Simplify the radical expression. \[ \sqrt{50} \]
Ask by Cummings Daniel. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\sqrt{50} = 5\sqrt{2}
\]
Solution
To simplify the radical expression \(\sqrt{50}\), follow these steps:
1. **Factor the Number Inside the Radical:**
Break down 50 into its prime factors:
\[
50 = 25 \times 2
\]
Here, 25 is a perfect square since \(25 = 5^2\).
2. **Apply the Square Root Property:**
The square root of a product is the product of the square roots:
\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}
\]
3. **Simplify the Square Root:**
Since \(\sqrt{25} = 5\), substitute this value:
\[
\sqrt{50} = 5 \times \sqrt{2} = 5\sqrt{2}
\]
**Final Simplified Form:**
\[
\sqrt{50} = 5\sqrt{2}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify \(\sqrt{50}\), we can breakdown the square root into its prime factors. Notice that \(50 = 25 \times 2\). Since \(25\) is a perfect square, we can take the square root of it out of the radical. Thus, \(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}\). So, the simplified form of \(\sqrt{50}\) is \(5\sqrt{2}\).
