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The Quadratic Formula
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Multiplication by 111
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Solving Systems of Equations - Two Lines
Solving Nonlinear Equations by Factoring
Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
Simplifying Complex Fractions
Factoring Trinomials
Linear Relations and Functions
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Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Fractions
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50


 
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Definition — Square Root

For a nonnegative real number, a, the principal square root of a is written If b is a nonnegative real number and b2 = a, then

Example:

because 7 is nonnegative and 72 = 49.

We can use geometry to provide a visual interpretation of a positive square root.

For example, suppose a square has an area of 25 square inches. The length of each side is the principal square root of the area. That is,

the length of a side of the square = = 5 inches.

A perfect square is a number that has a rational square root.

As we work with square roots, we will find it helpful to recognize perfect squares and their square roots. The table lists some whole number perfect squares and their principle square roots.

To approximate the square root of a number that is not a perfect square, we can estimate or use the key on a calculator.

Perfect Squares Principal Square Roots
02 = 0
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100

 

Property — Squares and Square Roots

English Squaring and taking a square root “undo” each other.

Algebra If a is a nonnegative real number, then

Example