Name: __________________________________________________________ Date: ___________ Period: _______________
Algebra 1
2.7 Find Square Roots and Compare Real Numbers
Vocabulary:
 Square Root — a number times itself to make the number you started with
 Radicand — the number under the radical symbol
 Perfect Square — the square of an integer

Irrational Number — a number that is not rational
 Real Number — the set of all rational and irrational numbers
EXAMPLE 1: Find Square Roots
Evaluate the expression:
a.
 36 = _____
The positive and negative square roots of 36 are __________
b.
49 = _____
The positive square root of 49 is _____
c.
 4 = _____
The negative square root of 4 is _____
GUIDED PRACTICE:
Evaluate the expression:
a.
 9 = _____
The negative square root of 9 is _____
b.
25 = _____
The positive square root of 25 is _____
c.
 64 = _____
The positive and negative square roots of 64 are _________
d.
 81 = _____
The negative square root of 81 is _____
EXAMPLE 2: Approximate a Square Root
The top of a folding table is a square whose area is 945 square inches. Approximate the side length of the tabletop to the nearest
inch.
SOLUTION:
You need to find the side length s of the tabletop such that s 2 = 945.
This means that s is the _________________________.
You can use a table to determine whether 945 is a perfect square.
Number
Square of
number
28
29
30
31
32
784
841
900
961
1024
As shown in the table, 945 __________ a perfect square. The greatest perfect
square less than 945 is _____. The least perfect square greater than 945 is ___.
Order Numbers: ___________________
Order Square Roots: ___________________
Order Simplified Square Roots: ___________________
945 is closer to _____ to _____.
Because 945 is closer to _____ than to 900,
The side length of the tabletop is about _____ inches.
GUIDED PRACTICE:
1.
Approximate the square root to the nearest integer:
32
You can use a table to determine whether 32 is a perfect square.
As shown in the table, 32 _______a perfect square. The greatest perfect square less than 32 is _____. The least perfect square
greater than 25 is _____.
Order Numbers: ___________________
Order Square Roots: ___________________
Order Simplified Square Roots: ___________________
32 is closer to _____ to _____.
Because 32 is closer to _____ than to _____,
2.
Approximate the square root to the nearest integer:
103
You can use a table to determine whether 103 is a perfect square.
Number
8
9
10
11
12
Square of
number
64
81
100
121
144
As shown in the table, 103 _____ a perfect square. The greatest perfect square less than 103 is _____. The least perfect square
greater than 100 is _____.
Order Numbers: ___________________
Order Square Roots: ___________________
Order Simplified Square Roots: ___________________
Because 103 is closer to _____ than to _____,
103 is closer to _____ to _____.
3.
Approximate the square root to the nearest integer:
 48
You can use a table to determine whether 48 is a perfect square.
As shown in the table, 48 _____ a perfect square. The greatest perfect square less than 48 is _____. The least perfect square
greater than 48 is _____.
Order Numbers: ___________________
Order Square Roots: ___________________
Order Simplified Square Roots: ___________________
Because 48 is closer to _____ than to _____,
4.
48 is closer to _____ than to _____.
Approximate the square root to the nearest integer:
 350
You can use a table to determine whether 350 is a perfect square.
As shown in the table, 350 _____ a perfect square. The greatest perfect square less than 350 is _____. The least perfect square
greater than 350 is _____.
Order Numbers: ___________________
Order Square Roots: ___________________
Order Simplified Square Roots: ___________________
Because 350 is closer to _____ than to _____,
 350 is closer to _____ than to _____.
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:
24, 100, 81
Real
Number Number?
Rational
Number?
Irrational Number?
Whole
Integer? Number?
24
100
81
EXAMPLE 4: Graph and order Real Numbers
4
Order the numbers from least to greatest: ,  5, 13, 2.5, 9
3
Solution:
Graph the numbers on a number line.
Read the numbers from left to right:
GUIDED PRACTICE:
1.
Order the numbers from least to greatest: 
9
,5.2,  20, 7, 4.1, 0
2
Begin by graphing the numbers on a number line.
Read the numbers from left to right:
2.
Classify the following numbers as Real, Rational, Irrational, Integer and/or Whole: 2.5,  5,
Real
Number Number?
-2.5
 5
4
3
9
13
Rational
Number?
Irrational Number?
Whole
Integer? Number?
4
, 9, 13
3