



Consider the surface area of a cube with side length s. The surface area is 6s^2. If the volume is 100, then s = 100^(1/3). What is the surface area in terms of 100?
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what is the cube root of 100
- (116/25)^3 = 1560896 / 15625 ≈ 99.897... which is quite close to 100.
- Can we express the cube root of one hundred as a continued fraction?
- How does the cube root function behave for values of x close to zero?
- How does its side length compare to a cube with volume 64 or 125?
- The radical notation $\sqrt\[3]{100}$ is often used when emphasizing the root operation, while the exponent notation $100^{1/3}$ is more convenient in algebraic manipulations.
- How would the side length change if we wanted a container with a volume of 200 cubic meters?
- What is the discriminant of x^3 - 100 = 0?
- What is a cube root modulo n?
- We can use continued fractions to find good rational approximations, but that's a bit involved for a quick answer.
- Also, the graphs of y = x^(1/n) for odd n have point symmetry about the origin, while for even n, the graphs (for non-negative x) do not have this symmetry (they might have symmetry about the y-axis if we consider x^n).
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