Question
\begin{tabular}{l|l|} & \multicolumn{2}{|c}{ Simplify, without using a calculator: } \\ .1 & \( \left(2 \frac{1}{2}\right)^{2}+(0,5)^{2} \)\end{tabular}
Ask by May Frank. in South Africa
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( 6.5 \).
Solution
Calculate or simplify the expression \( (2+1/2)^2+(0.5)^2 \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(2+\frac{1}{2}\right)^{2}+0.5^{2}\)
- step1: Add the numbers:
\(\left(\frac{5}{2}\right)^{2}+0.5^{2}\)
- step2: Convert the expressions:
\(\left(\frac{5}{2}\right)^{2}+\left(\frac{1}{2}\right)^{2}\)
- step3: Simplify:
\(\frac{5^{2}}{2^{2}}+\frac{1}{2^{2}}\)
- step4: Evaluate the power:
\(\frac{25}{4}+\frac{1}{2^{2}}\)
- step5: Evaluate the power:
\(\frac{25}{4}+\frac{1}{4}\)
- step6: Transform the expression:
\(\frac{25+1}{4}\)
- step7: Add the numbers:
\(\frac{26}{4}\)
- step8: Reduce the fraction:
\(\frac{13}{2}\)
The simplified expression \( \left(2 \frac{1}{2}\right)^{2}+(0,5)^{2} \) is equal to \( \frac{13}{2} \), \( 6\frac{1}{2} \), or \( 6.5 \).
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Simplify this solution The Deep Dive
To simplify \( \left(2 \frac{1}{2}\right)^{2}+(0.5)^{2} \), first convert \( 2 \frac{1}{2} \) to an improper fraction which equals \( \frac{5}{2} \). Now square it: \[ \left(\frac{5}{2}\right)^{2} = \frac{25}{4}. \] Next, compute \( (0.5)^{2} \): \[ (0.5)^{2} = 0.25 = \frac{1}{4}. \] Now add the two results: \[ \frac{25}{4} + \frac{1}{4} = \frac{26}{4} = \frac{13}{2}. \] So, the simplified expression is \( \frac{13}{2} \).
