Solve Equation Calculator Square Root

This calculator helps you solve equations involving square roots. Whether you're dealing with numerical square roots or solving for variables, this tool provides clear solutions and explanations.

How to Use This Calculator

To solve a square root equation:

Enter the equation in the input field. For example, you can enter expressions like √x = 5 or √(x + 3) = 2.
Select the type of equation you're solving (numerical or variable).
Click "Calculate" to see the solution.
Review the step-by-step solution provided.

The calculator will display the solution and explain each step of the process.

Formula Explained

Solving square root equations involves isolating the square root and then squaring both sides to eliminate the square root. The general steps are:

Isolate the square root term on one side of the equation.
Square both sides of the equation to remove the square root.
Solve the resulting equation for the variable.

Square Root Equation Formula

For an equation of the form √(ax + b) = c:

Square both sides: ax + b = c²
Solve for x: x = (c² - b)/a

This formula is used when solving for a variable in a square root equation.

Worked Examples

Example 1: Solving √x = 5

Square both sides: x = 5² → x = 25
Solution: x = 25

Example 2: Solving √(2x + 3) = 4

Square both sides: 2x + 3 = 16
Subtract 3: 2x = 13
Divide by 2: x = 6.5
Solution: x = 6.5

Frequently Asked Questions

What is a square root equation?: A square root equation is an equation that contains a square root of a variable or expression. Examples include √x = 5 or √(x + 3) = 2.
How do I solve a square root equation?: To solve a square root equation, isolate the square root term, square both sides of the equation, and then solve for the variable.
Can I solve square root equations with negative numbers?: Square root equations typically involve non-negative numbers since the square root of a negative number is not a real number. Solutions must be checked to ensure they satisfy the original equation.
What if the equation has a square root on both sides?: If the equation has square roots on both sides, you can square both sides to eliminate the square roots, but you must be careful to consider all possible solutions and check for extraneous roots.