Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$\sqrt{C}-15=37$
Answer (1)
Add 15 to both sides of the equation: C = 52 .
Square both sides of the equation: C = 5 2 2 .
Calculate 5 2 2 : C = 2704 .
The solution is 2704 .
Explanation
Understanding the Problem We are given the equation C − 15 = 37 and we want to solve for C .
Isolating the Square Root First, we isolate the square root term by adding 15 to both sides of the equation: C − 15 + 15 = 37 + 15 C = 52
Eliminating the Square Root Next, we square both sides of the equation to eliminate the square root: ( C ) 2 = ( 52 ) 2 C = 5 2 2
Calculating the Value of C Now, we calculate 5 2 2 : C = 52 × 52 = 2704
Final Answer Therefore, the solution is C = 2704 . Since the question asks us to round to two decimal places if necessary, and 2704 is an integer, we can write it as 2704.00.
Examples
Imagine you are designing a square garden and you know the length of the fence needed for one side is related to the area by the equation A − 15 = 37 , where A is the area of the garden. Solving this equation allows you to determine the exact area of the garden you can enclose with the available fencing. This type of problem is also applicable in physics, where the square root of a variable might represent a physical quantity, and solving for the variable gives you a concrete value for your calculations.
