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Multiplying by 11
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The Discriminant
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Rotating a Hyperbola
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BEDMAS & Fractions
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Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
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Simple Trinomials as Products of Binomials
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Graphing Equations in Three Variables
Properties of Exponents
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Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
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Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
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Powers and Roots of Complex Numbers
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What the Factored Form of a Quadratic can tell you about the graph
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Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
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Adding and Subtracting Rational Expressions
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
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Factoring Trinomials
Introduction to Fractions
Square Roots
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Square Roots

Definition of Square Root

Before we define the square root of a number, let’s review what we mean by the square of a number.

• The square of 5 is 52, which is 25.

• The square of -5 is (-5)2, which is also 25.

Now we will reverse the squaring process and obtain the square roots of a number.

The square root of a number is a number that when multiplied by itself, gives the original number.

The number 25 has two square roots, -5 and -5. Squaring 5 gives 25, squaring -5 also gives 25.

Each positive real number has two square roots, one positive and the other negative.

The positive square root of a number is called the principal square root. The principal square root of 25 is +5.

The radical symbol, , is used to denote the principle square root of a number.

For example,

The negative of the radical symbol, , denotes the negative square root.

For example,


The number 0 has a single square root, 0.

A negative real number, for example -25, does not have square roots that are real numbers. That’s because a real number times itself always gives a nonnegative number.

52 = +25 (-5)2 = -25


The expression under the radical symbol is called the radicand.

For example, in the expression , the radicand is 49.

A radical is the part of an expression that consists of a radical symbol and a radicand. In this example, the radical is

A radical expression is an expression that contains a radical.

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