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Square Roots and Radical Expressions
Solving Radical Equations
Simplifying Radical Expressions
Irrational Numbers in General and Square Roots in Particular
Roots of Polynomials
Simplifying Radical Expressions
Exponents and Radicals
Products and Quotients Involving Radicals
Roots of Quadratic Equations
Radical Expressions
Radicals and Rational Exponents
Find Square Roots and Compare Real Numbers
Radicals
Radicals and Rational Exponents
Theorems on the Roots of Polynomial Equations
SYNTHETIC DIVISION AND BOUNDS ON ROOTS
Simplifying Radical Expressions
Exponents and Radicals
Properties of Exponents and Square Roots
Solving Radical Equations
Rational Exponents and Radicals,Rationalizing Denominators
Rational Exponents and Radicals,Rationalizing Denominators
Quadratic Roots
Exponents and Roots
Multiplying Radical Expressions
Exponents and Radicals
Solving Radical Equations
Solving Quadratic Equations by Factoring and Extracting Roots
Newton's Method for Finding Roots
Roots of Quadratic Equations Studio
Roots, Radicals, and Root Functions
Review division factoring and Root Finding
Radicals
Simplifying Radical Expressions
Multiplying and Simplifying Radical Expressions
LIKE RADICALS
Multiplication and Division of Radicals
Radical Equations
BOUNDING ROOTS OF POLYNOMIALS
   
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Find Square Roots and Compare Real Numbers

Goal • Find square roots and compare real numbers.

Your Notes

VOCABULARY
Square root If b^2=a, then b is a square root of a. Square roots are written with the radical symbol .
Radicand The number or expression inside the radical symbol
Perfect square A number whose square roots are integers
Irrational number A number that cannot be written as the quotient of two integers
Real number The set of all rational and irrational numbers
SQUARE ROOT OF A REAL NUMBER

Words

If b^2=a, then b is a square root of a .

Example

5^2 = 25 and (-5)^2 = 25, so 5 and -5 are square roots of 25.

Your Notes

Example 1 Find square roots

All positive real
numbers have
two square roots,
a positive and a
negative square
root. The positive
square root is
called the principal
square root.
Evaluate the expression.

Solution

 
The negative square root of
36 is 26 .

The positive square root of
16 is 4

The positive and negative square roots
of 64 are 8 and 28 .

 

Guided Practice Evaluate the expression.

Example 2 Classify numbers

Tell whether each of the following numbers is a real number, a rational number, an irrational number, an
integer, or a whole number:

Solution

Number Real
Number ?
Rational
Number?
Irrational
Number ?
Integer ? Whole
Number ?
Yes Yes No Yes Yes
Yes Yes No Yes No
Yes No Yes No No

Your Notes

Example 3 Graph and order real numbers

Order the numbers from least to greatest:

Solution
Begin by graphing the numbers on a number line.

Read the numbers from left to right:

Guided Practice Complete the following exercises.

3. Tell whether each of the following numbers is a real number, rational number, irrational number, integer,
or whole number:

Real number:
Rational number:
Irrational number:
Integer:
Whole number:

Homework

4. Order the numbers from Exercise 3 from least to greatest.

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