Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$\sqrt[3]{C}+2=34$
Answer (1)
Subtract 2 from both sides: 3 C = 32 .
Cube both sides: C = 3 2 3 .
Calculate 3 2 3 : C = 32768 .
The solution is 32768 .
Explanation
Understanding the Problem We are given the equation 3 C + 2 = 34 and asked to solve for C . This involves isolating C by performing inverse operations.
Isolating the Cube Root First, we subtract 2 from both sides of the equation to isolate the cube root term: 3 C + 2 − 2 = 34 − 2 3 C = 32
Eliminating the Cube Root Next, we cube both sides of the equation to eliminate the cube root: ( 3 C ) 3 = ( 32 ) 3 C = 3 2 3
Calculating C Finally, we calculate 3 2 3 to find the value of C : C = 32 × 32 × 32 = 32768 Since the result is an integer, no rounding is necessary.
Final Answer Therefore, the solution to the equation 3 C + 2 = 34 is C = 32768 .
Examples
Imagine you are designing a cube-shaped container and you know that the cube root of its volume, plus 2, must equal 34. This equation helps you determine the exact volume the container needs to have. Understanding how to solve such equations is useful in various fields like engineering, architecture, and even in everyday tasks like calculating dimensions for DIY projects. For instance, if you need a cubic box and know that 3 V + 2 = 34 , solving for V gives you the required volume.
