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How to Solve Equations With the Square Root Principle

In mathematics, an exponent denotes the number of times a number (called the base) should be multiplied by itself. For example, 5^3 equals 5 * 5 *5. Every algebraic operation has an opposite. Addition has subtraction and division has multiplication. The opposite of exponents are roots or radicals. The lowest root is the square root, denoted with the symbol √. The square root is the opposite of the exponent 2 or a base raised to the second power.

Instructions

- 1
  Solve an equation containing a square exponent by eliminating the exponent using the square root principle, which states that if x^2 = k, then x = ±√(k). Note that the plus or minus symbol represents the positive or negative answers that are possible due to the fact that two negative numbers multiplied creates a positive.
- 2
  Solve the equation (x - 4)^2 + 2 = 18. Subtract 2 from both sides: (x - 4)^2 = 16. Take the square root of both sides to eliminate the exponent: (x - 4) = ±√16. Simplify: x - 4 = ± 4.
- 3
  Write out the equation in two ways, one each for the positive and negative possibilities of the 4 on the right side: x - 4 = 4 and x - 4 = -4. Add 4 to both sides of each equation to isolate the variable: x = 8 or x = 0.

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