Solve each equation.
1) [tex]3=\sqrt{b-1}[/tex]
Answer (2)
Square both sides of the equation to eliminate the square root: ( b − 1 ) 2 = 3 2 .
Simplify the equation: b − 1 = 9 .
Add 1 to both sides to isolate b : b = 9 + 1 .
Solve for b : b = 10 , so the final answer is 10 .
Explanation
Understanding the Problem We are given the equation 3 = b − 1 and we want to solve for b . This involves isolating b by performing algebraic operations on both sides of the equation.
Squaring Both Sides To eliminate the square root, we square both sides of the equation: ( b − 1 ) 2 = 3 2
Simplifying the Equation Simplifying both sides, we get: b − 1 = 9
Isolating b To isolate b , we add 1 to both sides of the equation: b = 9 + 1
Solving for b Therefore, the solution is: b = 10
Examples
Imagine you are designing a square garden and you know the area you want it to cover. If the area is represented by the equation A = s 2 , where A is the area and s is the side length, solving for s would involve taking the square root. Similarly, if you knew that the side length minus 1 has a square root of 3, you would solve the equation s − 1 = 3 to find the side length. This type of problem is useful in various scenarios such as calculating dimensions, determining speeds, or understanding growth rates where square roots are involved.
To solve the equation 3 = b − 1 , we square both sides to eliminate the square root, leading to b − 1 = 9 . After adding 1 to both sides, we find that b = 10 . Thus, the final answer is b = 10 .
;
