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	Solving Linear Systems of Equations by Elimination
	Solving Systems of Equation by Substitution and Elimination
	Polynomial Equations
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	Quadratic Functions
	Solving Proportions
	Parallel and Perpendicular Lines
	Simplifying Square Roots
	Simplifying Fractions
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	Adding and Subtracting Fractions
	Solving Linear Equations
	Inequalities in one Variable
	Recognizing Polynomial Equations from their Graphs
	Scientific Notation
	Factoring a Sum or Difference of Two Cubes
	Solving Nonlinear Equations by Substitution
	Solving Systems of Linear Inequalities
	Arithmetics with Decimals
	Finding the Equation of an Inverse Function
	Plotting Points in the Coordinate Plane
	The Product of the Roots of a Quadratic
	Powers
	Solving Quadratic Equations by Completing the Square

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Powers

The Principle of Powers

A radical equation is an equation in which a variable appears in a radicand.

For example, the variable x is in the radicand of the following radical equations:

To solve a radical equation, we will use the Principle of Powers.

Principle â€” Principle of Powers

If a = b, then aⁿ = bⁿ

Here, a, b, and n are real numbers.

While the Principle of Powers is true for all real numbers, the reverse is not always true. That is, if aⁿ = bⁿ then a = b may or may not be true.

For example, consider the following equations.

	Equation A		Equation B
Original equation.		= 5		= -5
Square both sides.		= (5)²		= (-5)²
Simplify.	x	= 25	x	= 25

Note that is the principle or positive square root of x. This is a positive number or zero.

For example,

The solution of Equation A, x = 25, checks since

However, the solution of Equation B, x = 25, does NOT check since

Squaring both sides of Equation B introduced an extraneous solution or false solution. Thus, when solving a radical equation we must check the answer to verify that it satisfies the original equation.

Note:

The negative square root of x is written as -. This is a negative number.

For example,