Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$\sqrt[3]{B}=-15$
Answer (1)
Cube both sides of the equation: ( 3 B ) 3 = ( − 15 ) 3 .
Simplify the equation: B = ( − 15 ) 3 .
Calculate the value of B : B = − 3375 .
The solution is − 3375 .
Explanation
Understanding the Problem We are given the equation 3 B = − 15 and asked to solve for B . This means we need to isolate B on one side of the equation.
Cubing Both Sides To isolate B , we need to eliminate the cube root. We can do this by cubing both sides of the equation: ( 3 B ) 3 = ( − 15 ) 3
Calculating the Value of B Simplifying the left side, we get B . On the right side, we have ( − 15 ) 3 = − 15 × − 15 × − 15 . Calculating this, we have − 15 × − 15 = 225 , and then 225 × − 15 = − 3375 . Therefore, B = − 3375
Final Answer Thus, the solution to the equation 3 B = − 15 is B = − 3375 .
Examples
Imagine you are designing a cube-shaped container for a liquid. If you know the cube root of the volume of the container is -15 (negative because it relates to a coordinate system), you can find the actual volume by cubing -15. This calculation helps determine the amount of liquid the container can hold. Understanding cube roots and cubing is essential in various fields, including engineering and architecture, for calculating volumes and dimensions.
