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Lesson #6
Supplemental Section: Find Square Roots and Compare Real Numbers
Key Vocabulary
Square Root: If b 2  a , then b is a square root of a.
So, since 5 2  25 , then 5 is a square root of 25.

Square roots are written with the radical symbol ______.

All positive real numbers have ____ square roots, a __________________ square root and a
____________________ square root.

Zero has only 1 square root, _______.

____________________ numbers do not have real square roots.
Note: When we see the
symbol, we only consider the positive square root BUT we take the sign in
front of the symbol if one is present!
Example 1: Evaluate each expression.
a)  36
b)
49
c)  4
d)
289
Hit the 2nd key,
then this key to
get the square
root.
Perfect Square: A number whose square roots are _________________________________________.
Recall: What are some examples of integers? ______________________________________________
Create a perfect square chart!!!
Example 2: Approximate a square root
The top of a folding table is a square whose area is 200 square inches. Approximate the side length of
the tabletop to the nearest inch.
On Your Own: Approximate the square root to the nearest integer. (Refer to list of perfect squares calculator)
1)
3)  48
2) 103
32
4)  85
Irrational Numbers:
The decimal form of an irrational number neither _________________ nor __________________.
Square roots of whole numbers that are not perfect squares are irrational!!!
Real Numbers: The set of all ______________________ and ________________________ numbers.
Let’s create a Venn diagram to help illustrate the real number system.
Real Numbers
Example 3: 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 after they are simplified.
Number
Real number?
Rational
number?
Irrational
number?
Integer?
Whole
number?
24
100
 81
5
Example 4: Graph and order real numbers
Using the numbers in the table above, order the numbers in the table from least to greatest and plot on a
number line.
Homework: Lesson #6 WORKSHEET #3-7 odd, 13-19 odd, 23, 25, 35, 37, 47, 48
Find Square Roots and Compare Real Numbers
Lesson #6: HOMEWORK