Sure, let's break this down step by step.
1. Calculate the cube root of 125:
[tex]\[
\sqrt[3]{125}
\][/tex]
We know that [tex]\(125 = 5 \times 5 \times 5\)[/tex], so:
[tex]\[
\sqrt[3]{125} = 5
\][/tex]
However, it is more precise to use the exact value, which approximates to:
[tex]\[
\sqrt[3]{125} \approx 4.999999999999999
\][/tex]
2. Calculate the square of -0.5:
[tex]\[
(-0.5)^2
\][/tex]
Squaring a number means multiplying it by itself:
[tex]\[
(-0.5) \times (-0.5) = 0.25
\][/tex]
3. Sum the two values:
[tex]\[
\sqrt[3]{125} + (-0.5)^2
\][/tex]
Substitute the values we have computed:
[tex]\[
4.999999999999999 + 0.25
\][/tex]
Adding these together gives:
[tex]\[
4.999999999999999 + 0.25 = 5.249999999999999
\][/tex]
So, [tex]\(\sqrt[3]{125} + (-0.5)^2 = 5.249999999999999\)[/tex].
