Question
Show all of your steps for how to simplify 35–√⋅210−−√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) BoldItalicUnderlineIncrease indentDecrease indentFormula keypad
Answers
GPT-4o mini
To simplify the expression \( 35 - \sqrt{210} \), we'll break down the steps systematically.
Given:
\[
35 - \sqrt{210}
\]
### Step 1: Check if \( \sqrt{210} \) can be simplified
First, we'll factor \( 210 \):
\[
210 = 2 \times 3 \times 5 \times 7
\]
Since none of these factors are perfect squares, \( \sqrt{210} \) cannot be simplified further.
### Step 2: Combine the terms
The expression is already combined in its simplest form, as \( 35 \) is a whole number and \( \sqrt{210} \) is a radical. They cannot be combined together into a single term since they are not like terms.
### Final Expression
Thus, the expression remains:
\[
35 - \sqrt{210}
\]
### Conclusion
The simplest radical form of the expression is:
\[
\boxed{35 - \sqrt{210}}
\]
Given:
\[
35 - \sqrt{210}
\]
### Step 1: Check if \( \sqrt{210} \) can be simplified
First, we'll factor \( 210 \):
\[
210 = 2 \times 3 \times 5 \times 7
\]
Since none of these factors are perfect squares, \( \sqrt{210} \) cannot be simplified further.
### Step 2: Combine the terms
The expression is already combined in its simplest form, as \( 35 \) is a whole number and \( \sqrt{210} \) is a radical. They cannot be combined together into a single term since they are not like terms.
### Final Expression
Thus, the expression remains:
\[
35 - \sqrt{210}
\]
### Conclusion
The simplest radical form of the expression is:
\[
\boxed{35 - \sqrt{210}}
\]