Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

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Square Roots

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


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