If [tex]$\sqrt{x}+6=16$[/tex], then [tex]$x$[/tex] could equal
A. 1
B. 4
C. 10
D. 100
Answer (1)
Isolate the square root term: x = 16 − 6 = 10 .
Square both sides to solve for x : x = 1 0 2 = 100 .
Verify the solution is among the given options.
The solution is 100 .
Explanation
Understanding the Problem We are given the equation x + 6 = 16 and asked to find the value of x .
Isolating the Square Root First, we need to isolate the square root term. To do this, we subtract 6 from both sides of the equation: x + 6 − 6 = 16 − 6 x = 10
Solving for x Now, to solve for x , we square both sides of the equation: ( x ) 2 = 1 0 2 x = 100
Checking the Solution Finally, we check if our solution is among the possible values given in the problem. The possible values are 1, 4, 10, and 100. Our solution, x = 100 , is among these values.
Examples
Imagine you are designing a square garden and you know that the length of the fence needed for one side, after adding an extra 6 feet for a decorative border, is 16 feet. This problem helps you calculate the actual area of the garden without the border. By solving the equation, you find the side length of the garden and then calculate the area, which is useful for planning how many plants you can fit in your garden. This kind of algebraic thinking is essential in many practical design and planning scenarios.
