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How to Take the Square Root of Both Sides of an Equation

Simple linear equations contain only one variable and numbers. The purpose of the equation is to isolate the variable on one side of the equal sign to provide a solution for that unknown value. Isolating the variable happens through using algebra to shift other terms away from the variable. This is done by applying the mathematical opposites of the terms. The opposite of addition is subtraction. The opposite of multiplication is division. And the opposite of exponents are roots.

Instructions

- 1
  Eliminate a squared exponent on a variable by taking the square root of both sides of the equation. Begin by moving all other terms away from the variable, to the other side of the equation, and simplifying where possible. Take the square root of both sides and simplify where possible.
- 2
  For example, solve the equation 3x^2 + 6 = 18. Begin to isolate the variable by subtracting 6 from both sides: 3x^2 + 6 - 6 = 18 - 6 becomes 3x^2 = 12. Divide both sides by 3: 3x^2 / 3 = 12 / 3 becomes x^2 = 4.
- 3
  Eliminate the exponent by taking the square root of both sides of the equation: √(x^2) = √4 becomes x = √4. Simplify the answer: x = 2.

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