Question
Look at this equation: \[ c^{3}=729 \] What is \( c \), the cube root of 729 ? \( c=\square \)
Ask by Mccoy Knight. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( c = 9 \)
Solution
1. We start with the given equation:
\[
c^3 = 729
\]
2. To solve for \( c \), we take the cube root of both sides:
\[
c = \sqrt[3]{729}
\]
3. We recognize that \( 9^3 = 9 \times 9 \times 9 = 729 \).
4. Therefore, the cube root of 729 is:
\[
c = 9
\]
\(\boxed{9}\)
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Simplify this solution Bonus Knowledge
Did you know that finding the cube root of a number like 729 can be visualized with cubes? Imagine a cube where each side measures 9 units. When you calculate the volume of this cube, you'll find it's \( 9 \times 9 \times 9 = 729 \). So, the cube root \( c \) is simply 9! In the world of mathematics, cube roots have practical applications too! For example, if you're trying to determine the volume of a specific object or measure how much material is needed for a cube-shaped box, calculating the cube root allows you to find the side length. In this case, since \( c = 9 \), you know that your box would have sides of 9 units each!
