Question
\( x=\frac{5^{2}-\sqrt[3]{27}+\sqrt[4]{49}}{25-2(10)} \) Round off your answer to TWO decimal
Ask by Smith Rojas. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x \approx 4.93 \)
Solution
Calculate or simplify the expression \( (5^{2}-\sqrt[3]{27}+\sqrt[4]{49})/(25-2(10)) \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(5^{2}-\sqrt[3]{27}+\sqrt[4]{49}\right)}{\left(25-2\times 10\right)}\)
- step1: Remove the parentheses:
\(\frac{5^{2}-\sqrt[3]{27}+\sqrt[4]{49}}{25-2\times 10}\)
- step2: Simplify the root:
\(\frac{5^{2}-3+\sqrt[4]{49}}{25-2\times 10}\)
- step3: Simplify the root:
\(\frac{5^{2}-3+\sqrt{7}}{25-2\times 10}\)
- step4: Multiply the numbers:
\(\frac{5^{2}-3+\sqrt{7}}{25-20}\)
- step5: Calculate:
\(\frac{22+\sqrt{7}}{25-20}\)
- step6: Subtract the numbers:
\(\frac{22+\sqrt{7}}{5}\)
The value of \( x \) is approximately 4.92915 when rounded to two decimal places.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
First, let's simplify the expression for \( x \): 1. Calculate \( 5^{2} \) which is \( 25 \). 2. Calculate \( \sqrt[3]{27} \) which is \( 3 \). 3. Calculate \( \sqrt[4]{49} \) which is \( 7 \). 4. Now plug these values back into the equation: \( x = \frac{25 - 3 + 7}{25 - 20} \) 5. Simplifying the numerator: \( 25 - 3 + 7 = 29 \) 6. Simplifying the denominator: \( 25 - 20 = 5 \) Now, computing \( x \): \[ x = \frac{29}{5} = 5.8 \] Rounding off to two decimal places, the answer is \( \boxed{5.80} \).
