Sure, let's solve the given expression step by step.
The given expression is:
[tex]\[ 200 + 8 \sqrt{200} - 2 \sqrt{363} \][/tex]
Step 1: Calculate [tex]\(8 \sqrt{200}\)[/tex]
First, we need to calculate [tex]\(\sqrt{200}\)[/tex]:
[tex]\[
\sqrt{200} \approx 14.1421
\][/tex]
Then we multiply by 8:
[tex]\[
8 \times 14.1421 \approx 113.1371
\][/tex]
So,
[tex]\[
8 \sqrt{200} \approx 113.1371
\][/tex]
Step 2: Calculate [tex]\(-2 \sqrt{363}\)[/tex]
Next, we need to calculate [tex]\(\sqrt{363}\)[/tex]:
[tex]\[
\sqrt{363} \approx 19.0526
\][/tex]
Then we multiply by -2:
[tex]\[
-2 \times 19.0526 \approx -38.1051
\][/tex]
So,
[tex]\[
-2 \sqrt{363} \approx -38.1051
\][/tex]
Step 3: Sum all the parts
Now, we combine all the calculated parts:
[tex]\[
200 + 113.1371 - 38.1051
\][/tex]
First, add [tex]\(200\)[/tex] and [tex]\(113.1371\)[/tex]:
[tex]\[
200 + 113.1371 \approx 313.1371
\][/tex]
Then, subtract [tex]\(38.1051\)[/tex] from [tex]\(313.1371\)[/tex]:
[tex]\[
313.1371 - 38.1051 \approx 275.0320
\][/tex]
Therefore, the final result of the expression [tex]\(200 + 8 \sqrt{200} - 2 \sqrt{363}\)[/tex] is approximately [tex]\(275.0320\)[/tex].
