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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
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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 Using the Square Root Property
The Slope of a Line
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What the Factored Form of a Quadratic can tell you about the graph
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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
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Solving Quadratic Equations by Completing the Square
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Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
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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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