Question
Show all of your steps for how to simplify 35–√⋅210−−√ . Your final answer should be in simplest radical form (not a decimal). Responses that are an answer only with no work shown will not receive credit.(6 points)
Answers
GPT-4o mini
To simplify \( 35 - \sqrt{210} \), we can follow these steps:
1. **Identify if \( \sqrt{210} \) can be simplified**:
- First, we factor \( 210 \) to see if it contains any perfect squares:
\[
210 = 2 \times 3 \times 5 \times 7
\]
Since none of the factors are perfect squares, \( \sqrt{210} \) cannot be simplified further.
2. **Write the expression clearly**:
The expression remains \( 35 - \sqrt{210} \).
3. **Final Expression**:
Since \( \sqrt{210} \) is already in its simplest form and cannot be simplified, we write:
\[
\text{Final answer: } 35 - \sqrt{210}
\]
Thus, the expression \( 35 - \sqrt{210} \) is already in simplest radical form.
1. **Identify if \( \sqrt{210} \) can be simplified**:
- First, we factor \( 210 \) to see if it contains any perfect squares:
\[
210 = 2 \times 3 \times 5 \times 7
\]
Since none of the factors are perfect squares, \( \sqrt{210} \) cannot be simplified further.
2. **Write the expression clearly**:
The expression remains \( 35 - \sqrt{210} \).
3. **Final Expression**:
Since \( \sqrt{210} \) is already in its simplest form and cannot be simplified, we write:
\[
\text{Final answer: } 35 - \sqrt{210}
\]
Thus, the expression \( 35 - \sqrt{210} \) is already in simplest radical form.