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.
