To solve the expression [tex]\(\left(2 \frac{1}{2}\right)^2 + (0.5)^2\)[/tex], let's break it down step-by-step.
1. Convert the mixed number to an improper fraction or a decimal:
The mixed number [tex]\(2 \frac{1}{2}\)[/tex] can be converted to a decimal. [tex]\(2 \frac{1}{2} = 2 + \frac{1}{2} = 2.5\)[/tex].
2. Square each number:
- Square [tex]\(2.5\)[/tex]:
[tex]\[
(2.5)^2 = 2.5 \times 2.5 = 6.25
\][/tex]
- Square [tex]\(0.5\)[/tex]:
[tex]\[
(0.5)^2 = 0.5 \times 0.5 = 0.25
\][/tex]
3. Add the squares together:
[tex]\[
6.25 + 0.25 = 6.5
\][/tex]
Therefore, [tex]\(\left(2 \frac{1}{2}\right)^2 + (0.5)^2 = 6.5\)[/tex].
So, our detailed steps give us the result:
1. [tex]\((2.5)^2 = 6.25\)[/tex]
2. [tex]\((0.5)^2 = 0.25\)[/tex]
3. [tex]\(6.25 + 0.25 = 6.5\)[/tex]
Thus, the final answer is:
[tex]\[
6.5
\][/tex]
