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Exponents and Radicals
Division of Radicals
Exponents and Radicals
RADICALS & RATIONAL EXPONENTS
Radicals and Rational Exponents
Radical Equations
Solving Radical Equations
Roots and Radicals
RADICAL EQUATION
Simplifying Radical Expressions
Radical Expressions
Solving Radical Equations
Solving Radical Equations
Exponents and Radicals
Exponents and Radicals
Roots;Rational Exponents;Radical Equations
Solving and graphing radical equations
Solving Radical Equations
Radicals and Rational Exponents
exponential_and_radical_properties
Roots, Radicals, and Root Functions
Multiplication of Radicals
Solving Radical Equations
Radical Expressions and Equations
SOLVING RADICAL EQUATIONS
Equations Containing Radicals and Complex Numbers
Square Roots and Radicals
Solving Radical Equations in One Variable Algebraically
Polynomials and Radicals
Roots,Radicals,and Fractional Exponents
Adding, Subtracting, and Multiplying Radical Expressions
Square Formula and Powers with Radicals
Simplifying Radicals
Exponents and Radicals Practice
Solving Radical Equations
Solving Radical Equations
Solving Radical Equations
Lecture-Radical Expressions
Radical Functions
   
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Exponents and Radicals

Combining Radical Expressions
Radical expressions can only be combined if there are like terms-terms with the same index and same radicand
(the expression inside the radical).

In the above expression, the terms with are alike and the terms with are alike. Therefore, the above
expressions simplifies as follows:

Notice that the two remaining terms are not alike and, hence, cannot be simplified.

Some terms which do not look alike at first glance may be alike after simplifying. Therefore, it is important
that you simplify all radicals before combining like terms.

Examples:


(note that these terms are NOT alike even though they both have a 10)

In simplifying we begin by using Property then simplifying and
rationalizing the denominator before combining:

(Note that 8 = 4 • 2)
(Multiply both by )

(now get a common denominator)

(now combine radicals)

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