Let's break down the expression [tex]\(\frac{\sqrt{555} + 5^2}{2^3 \times \sqrt[3]{222}}\)[/tex] into smaller, manageable parts and solve it step-by-step.
First, let's calculate the expressions in the numerator and the denominator separately.
1. Calculate [tex]\(\sqrt{555}\)[/tex]:
The square root of 555 is approximately [tex]\(23.5584\)[/tex].
2. Calculate [tex]\(5^2\)[/tex]:
[tex]\(5^2 = 25\)[/tex].
3. Calculate the numerator:
Add the results from steps 1 and 2:
[tex]\[
\sqrt{555} + 5^2 \approx 23.5584 + 25 = 48.5584
\][/tex]
4. Calculate [tex]\(2^3\)[/tex]:
[tex]\(2^3 = 8\)[/tex].
5. Calculate [tex]\(\sqrt[3]{222}\)[/tex]:
The cube root of 222 is approximately [tex]\(6.0550\)[/tex].
6. Calculate the denominator:
Multiply the results from steps 4 and 5:
[tex]\[
2^3 \times \sqrt[3]{222} \approx 8 \times 6.0550 = 48.4404
\][/tex]
Finally, divide the numerator by the denominator to find the result:
[tex]\[
\frac{\sqrt{555} + 5^2}{2^3 \times \sqrt[3]{222}} \approx \frac{48.5584}{48.4404} \approx 1.0024
\][/tex]
Therefore, the result of the given expression is approximately [tex]\(1.0024\)[/tex].
