Show all of your steps for how to simplify 35–√⋅210−−√

Question

. 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 can follow these steps:

1. Factor the Radicand (if possible): The expression has a radical, and we'll first analyze \( \sqrt{210} \) to see if we can simplify it.

   The number \( 210 \) can be factored into its prime factors: \[ 210 = 2 \times 3 \times 5 \times 7 \]

   None of these prime factors are perfect squares, which means \( \sqrt{210} \) cannot be simplified further.

2. Rewriting the Expression: Since \( \sqrt{210} \) is already in its simplest form, we continue with the expression.

   Therefore, the expression \( 35 - \sqrt{210} \) does not simplify further in terms of combining terms because \( 35 \) is a whole number and \( \sqrt{210} \) is an irrational number.

3. Final Answer: The expression \( 35 - \sqrt{210} \) is already in its simplest radical form. There are no further simplifications or factorizations that can be applied.

Thus, the final simplified answer is: \[ \boxed{35 - \sqrt{210}} \]