Solve $u^3=28$ where $u$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas.) $u=$
Answer (2)
Take the cube root of both sides of the equation u 3 = 28 to find u = 3 28 .
Factor 28 as 2 2 × 7 = 4 × 7 .
Simplify the cube root to u = 3 4 × 7 .
The simplified solution is 3 28 .
Explanation
Understanding the Problem We are given the equation u 3 = 28 , where u is a real number. Our goal is to solve for u and simplify the answer as much as possible.
Taking the Cube Root To solve for u , we take the cube root of both sides of the equation: u = 3 28
Simplifying the Cube Root Now, we simplify the cube root by factoring 28. We can write 28 as 28 = 4 × 7 = 2 2 × 7 . Therefore, u = 3 2 2 × 7 = 3 4 × 7 Since there are no perfect cube factors, the simplified form is u = 3 28 .
Final Answer Thus, the solution to the equation u 3 = 28 is u = 3 28 .
Examples
Imagine you are designing a cubic container that needs to hold 28 cubic units of volume. To find the length of each side of the container, you would need to solve the equation u 3 = 28 , where u represents the length of a side. The solution, u = 3 28 , gives you the exact length required for each side of the cubic container to achieve the desired volume. This concept is useful in various real-world applications, such as designing packaging, calculating material requirements for construction, or determining the dimensions of storage spaces.
The solution to the equation u 3 = 28 is u = 3 28 . This is the simplest form since there are no perfect cube factors in 28. Thus, we cannot simplify it further.
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