Question

Question
Subtract 823−−√−23−−√
. (1 point)
Responses

723−−√
7 start root 23 end root

823−−√
8 start root 23 end root

846−−√
8 start root 46 end root

746−−√

Answer 1

To calculate \( \sqrt{823} - \sqrt{23} \), we first approximate \( \sqrt{823} \).

Since \( 28^2 = 784 \) and \( 29^2 = 841 \), we know that \( \sqrt{823} \) is slightly less than 29 but greater than 28.

Now, approximate \( \sqrt{23} \):

Since \( 4^2 = 16 \) and \( 5^2 = 25 \), we know that \( \sqrt{23} \) is slightly less than 5 but greater than 4.

Now let's compute \( \sqrt{823} - \sqrt{23} \) using numerical values:

Assuming approximate values, we have:
- \( \sqrt{823} \approx 28.7 \)
- \( \sqrt{23} \approx 4.8 \)

Now subtracting these values:
\[
28.7 - 4.8 \approx 23.9
\]

However, we need the response in the format given in the options. We can combine the two square roots. The subtraction of square roots does not simplify neatly like addition or multiplication.

Thus, the answer is:
\[
\sqrt{823} - \sqrt{23}
\]

This does not match any response provided in a straightforward way.

However, if we reason with the closest option regarding numerical computation and possible square roots:
- The closest simplification for options would lead us to believe that \( \sqrt{846} \) or further rational investigation may lead there but requires root manipulation which does not lead to simple compounds of the provided values.

Therefore, the most simplified form we conclude on remains \( \sqrt{823} - \sqrt{23} \).

To summarize:
- "Subtract \( \sqrt{823} - \sqrt{23} \)" yields no straightforward selections;
- Final answer closest through approximation reasoning yet unlisted maintains toward options.

So the final response would logically imply we possibly assess through numerical subtraction however without concrete answer in options, we'd aim to select or assert categorically meant to derive from approximated roots or volume calculation formulas if further exploration in answer design.

The answer remains \( \sqrt{823} - \sqrt{23} \).
If we proceed numerically and approximate effectively amidst selections confined, we may adapt \( \sqrt{746} \) which would lend plausible bounds.

Thus, from your provided responses, the next closest viable response amidst offers would relate back to:

**Response**: 746−−√.