Questions: HONORS ALGEBRA I W/PROBABILITY 6-1: MathXL for School: Practice Problem-Solving Copy 1 Nov 15 - 11:59 pm Describe two ways to express the edge length of a cube with a volume shown. 2500 in.^3 Select all that apply. A. sqrt[3]2500 B. 2500^1/3 C. 2500^-3 D. 2500^3

Solution Steps

To find the edge length of a cube given its volume, we need to take the cube root of the volume. This can be expressed in two ways: using the cube root notation or using the exponent notation with a power of 1/3.

1. The edge length of a cube with volume \( V \) can be found by taking the cube root of \( V \).
2. This can be expressed as \( \sqrt[3]{V} \) or \( V^{\frac{1}{3}} \).

To find the edge length \( s \) of a cube with a volume \( V = 2500 \, \text{in}^3 \), we use the formula for the volume of a cube, which is given by:

\[ V = s^3 \]

To solve for \( s \), we take the cube root of the volume:

\[ s = \sqrt[3]{V} = \sqrt[3]{2500} \]

Calculating the cube root of \( 2500 \):

\[ s \approx 13.5721 \]

This value can also be expressed using exponent notation:

\[ s = 2500^{\frac{1}{3}} \approx 13.5721 \]

Final Answer