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Answer
الناتج تقريبياً هو 17.099759.
Solution
Calculate or simplify the expression \( \sqrt[3]{625}+\sqrt[3]{40}+\sqrt[3]{135} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt[3]{625}+\sqrt[3]{40}+\sqrt[3]{135}\)
- step1: Simplify the root:
\(5\sqrt[3]{5}+\sqrt[3]{40}+\sqrt[3]{135}\)
- step2: Simplify the root:
\(5\sqrt[3]{5}+2\sqrt[3]{5}+\sqrt[3]{135}\)
- step3: Simplify the root:
\(5\sqrt[3]{5}+2\sqrt[3]{5}+3\sqrt[3]{5}\)
- step4: Collect like terms:
\(\left(5+2+3\right)\sqrt[3]{5}\)
- step5: Add the numbers:
\(10\sqrt[3]{5}\)
The sum of \( \sqrt[3]{625}+\sqrt[3]{40}+\sqrt[3]{135} \) is approximately 17.099759.
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Simplify this solution Bonus Knowledge
To simplify \( \sqrt[3]{625}+\sqrt[3]{40}+\sqrt[3]{135} \), we can start by breaking down each term. First, \( \sqrt[3]{625} = \sqrt[3]{5^4} = 5\sqrt[3]{5} \). Next, we have \( \sqrt[3]{40} = \sqrt[3]{8 \cdot 5} = 2\sqrt[3]{5} \). Finally, \( \sqrt[3]{135} = \sqrt[3]{27 \cdot 5} = 3\sqrt[3]{5} \). Now, combining these results: \[ 5\sqrt[3]{5} + 2\sqrt[3]{5} + 3\sqrt[3]{5} = (5 + 2 + 3)\sqrt[3]{5} = 10\sqrt[3]{5}. \] Thus, the final answer is \( 10\sqrt[3]{5} \).
