Algebra Tutorials!
   
   
Home
Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
Functions
Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
Polynomial Equations
Solving Linear Systems of Equations by Graphing
Quadratic Functions
Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
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
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


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 — 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,

Copyrights © 2005-2019