Simplify, without using a calculator: $$ \left(2 \frac{1}{2}\right)^{2}+(0,5)^{2} $$

Question

UpStudy AI · Accepted Answer

1. Convert $$2 \frac{1}{2}$$ to an improper fraction:
$$
2 \frac{1}{2} = \frac{5}{2}
$$

2. Square the fraction:
$$
\left(\frac{5}{2}\right)^2 = \frac{25}{4}
$$

3. Interpret $$0,5$$ as $$0.5$$ which is:
$$
0.5 = \frac{1}{2}
$$

4. Square $$0.5$$:
$$
\left(\frac{1}{2}\right)^2 = \frac{1}{4}
$$

5. Add the results:
$$
\frac{25}{4} + \frac{1}{4} = \frac{26}{4}
$$

6. Simplify the fraction:
$$
\frac{26}{4} = \frac{13}{2}
$$
$$\frac{13}{2}$$

Simplify, without using a calculator: \( \left(2 \frac{1}{2}\right)^{2}+(0,5)^{2} \)