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Answer
La raíz cúbica de \(-\frac{729}{512}\) es \(-\frac{9}{8}\).
Solution
Calculate or simplify the expression \( \sqrt[3]{-\frac{729}{512}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt[3]{-\frac{729}{512}}\)
- step1: Use the properties of radicals:
\(-\sqrt[3]{\frac{729}{512}}\)
- step2: Use the properties of radicals:
\(-\frac{\sqrt[3]{729}}{\sqrt[3]{512}}\)
- step3: Simplify the expression:
\(-\frac{9}{8}\)
La raíz cúbica de \(-\frac{729}{512}\) es igual a \(-\frac{9}{8}\) o \(-1\frac{1}{8}\) o \(-1.125\).
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Simplify this solution Bonus Knowledge
Let's break it down! The cube root of a negative fraction involves taking the cube root of both the numerator and the denominator separately. So, we find the cube roots of -729 and 512. The cube root of -729 is -9, and the cube root of 512 is 8. Therefore, \( \sqrt[3]{-\frac{729}{512}} = \frac{-9}{8} \). How neat is that? Now, remember that when you deal with cube roots, negative and positive signs play a fun game. The cube root of a negative number remains negative, while squares and fourths can lead to those pesky imaginary numbers. So, embrace the cube root's rebellious nature—let it guide you through math with a twist!
