Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$\sqrt[5]{C}=2$
Answer (1)
Raise both sides of the equation to the power of 5: ( 5 C ) 5 = 2 5 .
Simplify the equation: C = 2 5 .
Calculate the value: C = 32 .
The solution is 32 .
Explanation
Understanding the Problem We are given the equation 5 C = 2 and we need to solve for C . This means we need to isolate C on one side of the equation.
Eliminating the Root To isolate C , we need to eliminate the fifth root. We can do this by raising both sides of the equation to the power of 5: ( 5 C ) 5 = 2 5
Simplifying the Equation Simplifying the left side, we get C . Now we need to calculate 2 5 . C = 2 5
Calculating the Power Calculating 2 5 , we have: 2 5 = 2 × 2 × 2 × 2 × 2 = 32 Therefore, C = 32 .
Final Answer Since the problem asks us to round to two decimal places if necessary, and 32 is already a whole number, we can write it as 32.00. Thus, the solution is C = 32 .
Examples
Imagine you are designing a cube-shaped container, and you know that the fifth root of its volume must be 2 units. This problem helps you determine the actual volume of the container. Understanding how to solve equations with radicals is crucial in various fields, such as engineering, physics, and computer graphics, where you often need to calculate volumes, areas, or other physical quantities based on given constraints.
