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.