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# Try our Free Online Math Solver! Online Math Solver

 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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# Other Types of Equations

Equations with Radical and Rational Exponents

When solving an equation linear in form with radicals or
rational exponents , simplify the equation, isolate the most
complicated radical on one side , and raise both sides to
the power equal to the index of the radical in order to
eliminate the last . You may need to repeat this procedure
if the resulting equation still contains a radical.

Note: We solve radical equations over the real numbers .

Caution! If you raise both sides of an equation to an
even power , the new equation may have more real
solutions than the original one.

Example: Equation x = 6 has solution set: {6}.
Raising both sides to the power 2, gives the equation
x^2 = 36 which has solution set x = ±6.
Thus, x = −6 is an extraneous solution to the original
equation and must be rejected.

Important! When raising to an even power, always
check each proposed solution in the original equation.

Example: Solve Example: Solve Note: If n is an even number, is never negative .

Example: Solve the equation Example: Solve the equation Example: Solve by using a substitution.  Example: Solve the equation in the complex number system Factorable Equations

Example: Find all solutions of the equation: Example: Solve by factoring Equations with Absolute Value

Recall:
1.|x| is the distance on the number line from 0 to x.
2.|x|≥ 0
3.|x|= 0 if and only if x = 0
4.|x|= −x

5. The algebraic definition : If a is a positive real number and u is any algebraic
expression , then
|u|= a is equivalent to u = a or u = −a .

Example: Solve the equations.    Prev Next