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)

Answer 1

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.