Solve X Square Root Calculator

This square root calculator solves for x in equations containing square roots. It handles both simple and more complex equations involving square roots, providing step-by-step solutions and visualizations.

How to Use This Calculator

To solve for x in a square root equation:

Enter your equation in the input field using the variable x. For example: √(x + 5) = 3
Click the "Calculate" button to solve the equation
View the solution in the result panel below the calculator
Review the step-by-step solution and any visualizations

This calculator handles equations where the square root is isolated or appears with other terms. For more complex equations, you may need to isolate the square root first.

Square Root Formula

The basic square root formula is:

√a = b ⇒ a = b²

For equations where the square root is not isolated, you'll need to isolate it first. For example:

√(x + 5) = 3 ⇒ x + 5 = 3² ⇒ x + 5 = 9 ⇒ x = 9 - 5 ⇒ x = 4

The calculator follows these steps automatically when you enter your equation.

Worked Examples

Example 1: Simple Square Root

Equation: √x = 5

Solution:

Square both sides: x = 5² ⇒ x = 25
Final answer: x = 25

Example 2: Square Root with Addition

Equation: √(x + 3) = 4

Solution:

Square both sides: x + 3 = 4² ⇒ x + 3 = 16
Solve for x: x = 16 - 3 ⇒ x = 13
Final answer: x = 13

Example 3: Square Root with Subtraction

Equation: √(x - 2) = 3

Solution:

Square both sides: x - 2 = 3² ⇒ x - 2 = 9
Solve for x: x = 9 + 2 ⇒ x = 11
Final answer: x = 11

Frequently Asked Questions

What types of square root equations can this calculator solve?: This calculator can solve equations where the square root is isolated or appears with addition or subtraction. It cannot solve equations with square roots in the denominator or more complex nested roots.
How do I solve for x when the square root is not isolated?: First isolate the square root by performing the same operation on both sides of the equation that would isolate the square root. Then square both sides to eliminate the square root.
What if the equation has a negative square root?: The calculator will provide the positive solution. Remember that square roots are defined to be non-negative in real numbers, so negative square roots don't have real solutions.
Can this calculator handle decimal solutions?: Yes, the calculator will provide decimal solutions when necessary, rounded to two decimal places for readability.
What if the equation has no solution?: The calculator will indicate that there is no real solution to the equation. This typically happens when the expression inside the square root becomes negative after solving.