Evaluate: √((45.4)² / ((3.2)² × (6.5)³))
Understand the Problem
The question is asking to evaluate the expression involving a square root and powers of numbers. We will calculate the value by simplifying the given expression step by step.
Answer
The evaluated expression is approximately $0.856$.
Answer for screen readers
The final answer is approximately $0.856$.
Steps to Solve
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Identify the Expression We need to evaluate the expression: $$ \sqrt{\frac{(45.4)^2}{(3.2)^2 \times (6.5)^3}} $$
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Calculate the Powers First, calculate the powers:
- ( (45.4)^2 = 2067.16 )
- ( (3.2)^2 = 10.24 )
- ( (6.5)^3 = 274.625 )
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Substitute the Values Now substitute these values back into the expression: $$ \sqrt{\frac{2067.16}{10.24 \times 274.625}} $$
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Calculate the Denominator Calculate the denominator: $$ 10.24 \times 274.625 = 2819.01 $$
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Form the Final Fraction Now we have: $$ \sqrt{\frac{2067.16}{2819.01}} $$
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Calculate the Fraction Evaluate the fraction: $$ \frac{2067.16}{2819.01} \approx 0.733 $$
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Calculate the Square Root Now, take the square root: $$ \sqrt{0.733} \approx 0.856 $$
The final answer is approximately $0.856$.
More Information
This expression combines the use of powers and square roots, demonstrating simplification techniques that can be useful in advanced mathematical concepts. The result is a rational number that represents the evaluated expression.
Tips
- Miscalculating Powers: Double-check the calculations for squaring and cubing numbers.
- Arithmetic Errors: Ensure careful multiplication in the denominator to avoid mistakes.
- Square Root Confusion: Remember to take the square root of the entire fraction, not just the numerator or the denominator.
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