Question
Simplify, without using a calculator: \( \left(2 \frac{1}{2}\right)^{2}+(0,5)^{2} \)
Ask by Watson French. in South Africa
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{13}{2}\)
Solution
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:
\[
\frac{26}{4} = \frac{13}{2}
\]
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Simplify this solution Bonus Knowledge
To simplify \( \left(2 \frac{1}{2}\right)^{2}+(0.5)^{2} \), we first convert \( 2 \frac{1}{2} \) into an improper fraction. \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2} \). Next, we square \( \frac{5}{2} \): \[ \left(\frac{5}{2}\right)^{2} = \frac{25}{4}. \] Now, we calculate \( (0.5)^{2} \): \[ (0.5)^{2} = 0.25 = \frac{1}{4}. \] Now we can add \( \frac{25}{4} \) and \( \frac{1}{4} \): \[ \frac{25}{4} + \frac{1}{4} = \frac{25 + 1}{4} = \frac{26}{4} = \frac{13}{2}. \] The simplified result is \( \frac{13}{2} \) or \( 6.5 \).
