Solve the equation $10+\sqrt{y}=14$
A) $y=4$
B) $y=576$
C) $y=16$
D) $y=2$
Answer (1)
Subtract 10 from both sides: y = 4 .
Square both sides: y = 16 .
The solution to the equation is 16 .
Explanation
Understanding the Problem We are given the equation 10 + y = 14 and asked to solve for y . Our goal is to isolate y on one side of the equation.
Isolating the Square Root First, we subtract 10 from both sides of the equation to isolate the square root term: 10 + y − 10 = 14 − 10 y = 4
Solving for y Next, we square both sides of the equation to eliminate the square root: ( y ) 2 = 4 2 y = 16
Final Answer Therefore, the solution to the equation is y = 16 .
Examples
Imagine you are calculating the side length of a square garden. If the area of the garden plus a 10 square meter shed equals 14 square meters, this problem helps you find the area of the garden alone. By understanding how to isolate variables and solve equations, you can determine the dimensions needed for your garden project. This skill is useful in various practical scenarios, from home improvement to landscape design.
