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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Simplifying Square Roots That Contain Variables

Next we will simplify a square-root radical whose radicand contains a variable.

Let’s look at these examples.

If x is a nonnegative real number, then:

since x · x = x2  
since (x3)2 = x6 Notice that
since (x5)2 = x10 Notice that
since (x8)2 = x16 Notice that
In each example, the exponent of the variable in the simplified expression is one-half the exponent of the variable in the radicand.

If the power of x in the radicand is not a multiple of 2, we rewrite the radicand as a product of x1 and an even power of x.

For example, let’s simplify where x is a nonnegative real number.
Write x37 as x36 · x1.
Write as the product of two radicals.
In the remainder of this Topic, we will assume that each variable under a radical represents a nonnegative real number.

Be careful:

If x is negative, then

For example, if x = -3:


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