Question
Simplify. \( \sqrt{125}+\sqrt{28}-8 \sqrt{5} \) \( [?] \sqrt{\square}-\square \sqrt{\square} \)
Ask by Franklin Griffin. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2\sqrt{7} - 3\sqrt{5} \)
Solution
To simplify the expression:
\[
\sqrt{125} + \sqrt{28} - 8 \sqrt{5}
\]
Let's break it down step by step.
1. **Simplify each square root:**
- \(\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}\)
- \(\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}\)
2. **Substitute the simplified forms back into the expression:**
\[
5\sqrt{5} + 2\sqrt{7} - 8\sqrt{5}
\]
3. **Combine like terms:**
- Combine the terms with \(\sqrt{5}\):
\[
5\sqrt{5} - 8\sqrt{5} = -3\sqrt{5}
\]
- The term with \(\sqrt{7}\) remains as is:
\[
2\sqrt{7}
\]
4. **Write the final simplified expression:**
\[
2\sqrt{7} - 3\sqrt{5}
\]
So, the expression in the desired format is:
\[
\boxed{2\,\sqrt{7}\ -\ 3\,\sqrt{5}}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
Sure! Let’s simplify \( \sqrt{125} + \sqrt{28} - 8\sqrt{5} \). First, we simplify \( \sqrt{125} \): \[ \sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5} \] Next, simplify \( \sqrt{28} \): \[ \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \] Now we can substitute these back into the original expression: \[ 5\sqrt{5} + 2\sqrt{7} - 8\sqrt{5} \] Now, we combine the like terms involving \(\sqrt{5}\): \[ (5 - 8)\sqrt{5} + 2\sqrt{7} = -3\sqrt{5} + 2\sqrt{7} \] Thus, the expression simplifies to: \[ 2\sqrt{7} - 3\sqrt{5} \] So, the final answer is: \[ 2\sqrt{7} - 3\sqrt{5} \] where \( [2] \sqrt{7} - [3] \sqrt{5} \).
