Question
2.2 Sinflify 2.2.1 \( 2.5^{2}\left(5^{3}+4.5^{2}+1\right) \)
Ask by Bond Long. in South Africa
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of \(2.5^{2}(5^{3}+4.5^{2}+1)\) is \(914.0625\).
Solution
Calculate or simplify the expression \( 2.5^{2}(5^{3}+4.5^{2}+1) \).
Calculate the value by following steps:
- step0: Calculate:
\(2.5^{2}\left(5^{3}+4.5^{2}+1\right)\)
- step1: Convert the expressions:
\(2.5^{2}\left(5^{3}+\left(\frac{9}{2}\right)^{2}+1\right)\)
- step2: Add the numbers:
\(2.5^{2}\times \frac{585}{4}\)
- step3: Convert the expressions:
\(\left(\frac{5}{2}\right)^{2}\times \frac{585}{4}\)
- step4: Evaluate the power:
\(\frac{5^{2}}{2^{2}}\times \frac{585}{4}\)
- step5: Multiply the fractions:
\(\frac{5^{2}\times 585}{2^{2}\times 4}\)
- step6: Multiply:
\(\frac{14625}{2^{4}}\)
- step7: Evaluate the power:
\(\frac{14625}{16}\)
The simplified form of \(2.5^{2}(5^{3}+4.5^{2}+1)\) is \(\frac{14625}{16}\) or \(914\frac{1}{16}\) or \(914.0625\).
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Simplify this solution Extra Insights
To simplify the expression \( 2.5^{2}\left(5^{3}+4.5^{2}+1\right) \), we begin by calculating \( 2.5^{2} \) which equals \( 6.25 \). Next, we evaluate the term inside the parentheses: First, \( 5^{3} = 125 \), then \( 4.5^{2} = 4 \times 25 = 100 \), and finally we add \( 1 \). So, \( 125 + 100 + 1 = 226 \). Now, multiplying \( 6.25 \) by \( 226 \) gives us: \( 6.25 \times 226 = 1412.5 \). Thus, the simplified expression is \( 1412.5 \).
