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EUESTION 1 \( 1.1 \quad \) Calculate the following WITH THE USE OF A CALCULATOR \( 1.1 .1 \quad \frac{\sqrt[3]{(1.9)^{2}+\frac{27^{4}}{3^{4}}}}{\pi} \)

Ask by Summers Sullivan. in South Africa
Feb 25,2025

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Answer

The result is approximately 5.960094.

Solution

Calculate or simplify the expression \( \frac{\sqrt[3]{(1.9)^{2}+\frac{27^{4}}{3^{4}}}}{\pi} \). Calculate the value by following steps: - step0: Calculate: \(\frac{\sqrt[3]{1.9^{2}+\frac{27^{4}}{3^{4}}}}{\pi }\) - step1: Convert the expressions: \(\frac{\sqrt[3]{\left(\frac{19}{10}\right)^{2}+\frac{27^{4}}{3^{4}}}}{\pi }\) - step2: Divide the terms: \(\frac{\sqrt[3]{\left(\frac{19}{10}\right)^{2}+9^{4}}}{\pi }\) - step3: Add the numbers: \(\frac{\sqrt[3]{\frac{656461}{100}}}{\pi }\) - step4: Simplify the root: \(\frac{\frac{\sqrt[3]{6564610}}{10}}{\pi }\) - step5: Multiply by the reciprocal: \(\frac{\sqrt[3]{6564610}}{10}\times \frac{1}{\pi }\) - step6: Multiply the fractions: \(\frac{\sqrt[3]{6564610}}{10\pi }\) The result of the expression \( \frac{\sqrt[3]{(1.9)^{2}+\frac{27^{4}}{3^{4}}}}{\pi} \) is approximately 5.960094.

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Simplify this solution

Mind Expander

To tackle this expression step by step, first calculate the numerator. Start by computing \( (1.9)^{2} \) which is roughly 3.61. Next, calculate \( 27^{4} \) which equals 531441. Then divide that by \( 3^{4} \) (which is 81) to yield approximately 6571. The whole expression in the numerator becomes \( \sqrt[3]{3.61 + 6571} \). After doing this calculation, divide the result by \( \pi \) to get the final value. Remember to double-check each calculation! For a clearer view, if you want to visualize this, consider plotting the function involved in your original expression. Graphing may reveal some interesting asymptotic behavior or where the function changes rapidly! This can be a fun way to understand how each component contributes to the overall calculation.

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