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How to Move a Square Root to the Other Side of an Equation

Algebraic operations have opposites. Addition is the opposite of subtraction, multiplication is the opposite of division and roots (also called radicals) are the opposite of exponents. The smallest root is the square root, denoted by the symbol √. The next highest root is the cube root, denoted with ³√. Larger roots can sometimes be simplified by extracting any perfect squares/cubes from the larger number and placing them in front. For example, √27 also equals √9 * √3, which simplifies to 3 * √3 or 3√3.

Instructions

- 1
  Solve a simple linear equation, containing one variable and numbers, using algebra to move the numbers away from the variable until it is isolated on one side of the equation. Move a square root to the other side of the equation to combine it with like terms, combining only if the numbers within the radicals match.
- 2
  Solve the equation 3√4 + 8 = 6x - 2√4. Note that although it would be possible to simplify the roots now, it is easier to first combine like terms. Add 2√4 to both sides: 3√4 + 2√4 + 8 = 6x - 2√4 + 2√4 becomes 5√4 + 8 = 6x. Perform the square root and multiply to the leading number: 5 * 2 = 10.
- 3
  Rewrite the equation: 10 + 8 = 6x. Combine like terms on the left: 18 = 6x. Divide both sides by 6: 3 = x.

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