Square Root Variables Calculator
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
This square root variables calculator helps you solve equations where the square root of a variable is involved. Whether you're studying algebra, physics, or engineering, understanding how to handle square roots of variables is essential.
What is a Square Root of a Variable?
The square root of a variable, often written as √x, represents a number that, when multiplied by itself, gives the original variable. For example, √9 = 3 because 3 × 3 = 9.
When dealing with equations involving square roots of variables, you'll often need to solve for x. This typically requires isolating the square root and then squaring both sides of the equation to eliminate the square root.
Key Formula
If √x = a, then x = a²
This is the fundamental principle for solving equations with square roots of variables.
How to Solve Square Root Equations with Variables
Solving equations with square roots of variables follows a systematic approach:
- Isolate the square root term on one side of the equation.
- Square both sides of the equation to eliminate the square root.
- Solve for the variable.
- Check your solution by substituting it back into the original equation.
Important Note
When solving √x = a, x must be non-negative because the square root of a negative number is not a real number. Always check that your solution satisfies the original equation.
Worked Examples
Example 1: Simple Square Root Equation
Solve for x in the equation: √x = 5
- Square both sides: (√x)² = 5² → x = 25
- Check: √25 = 5 (which is correct)
Example 2: Equation with Addition
Solve for x in the equation: √x + 3 = 7
- Isolate the square root: √x = 7 - 3 → √x = 4
- Square both sides: x = 16
- Check: √16 + 3 = 4 + 3 = 7 (which is correct)
FAQ
Can I solve √x = -3?
No, because the square root of a real number is always non-negative. There is no real solution to √x = -3.
What if the equation has a square root on both sides?
You can still solve it by isolating one square root and then squaring both sides. Just remember to check your solution in the original equation.
How do I solve √(x + 5) = 4?
First isolate the square root: √(x + 5) = 4. Then square both sides: x + 5 = 16. Finally, solve for x: x = 11.