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.

Answer 1

To simplify the expression \( 35 - \sqrt{210} \), we will first break it down into simpler steps and check the factors we can use to simplify \( \sqrt{210} \).

Step 1: Factor 210

The number \( 210 \) can be factored into its prime factors: \[ 210 = 2 \times 3 \times 5 \times 7 \] None of the factors of \( 210 \) are perfect squares, meaning \( \sqrt{210} \) cannot be simplified further in terms of radicals.

Step 2: Simplifying the Expression

Now we look at the expression: \[ 35 - \sqrt{210} \] Since we cannot simplify \( \sqrt{210} \) any further, the expression is already in its simplest form.

Step 3: Final Answer

Thus, the expression \( 35 - \sqrt{210} \) is already simplified, and the final answer in simplest radical form is: \[ \boxed{35 - \sqrt{210}} \]