Name_______________________________ Period___ 8R 13.6 Comparing and Ordering CLASS WORK
Estimating, Comparing and Ordering Square Roots
Review: List the first 15 perfect squares
____ , ____ ,_____ , ____ , ____ , ____ ,_____ , ____ ,_____ , ____ ,_____ ,_____ , ____ ,_____ ,_____
12
22
32
42
52
62
72
82
92
102 112
122 132
142
152
Vocabulary:
• Integers- whole numbers and their opposites (Ex: {….-3, -2, -1, 0, 1, 2, 3,…}
• Consecutive- one number right after another.
• Inequality Symbols<
Less Than
>
Greater Than
≤
Less than or equal to
≥
Greater than or equal to
To estimate the square root of a non-perfect square without a calculator:
Rule:
1. Find the closest perfect square less than the number
2. Find the closest perfect square greater than the number
3. The square root of the non-perfect square must be between the square root of these two perfect squares
Examples:
Find the two consecutive whole numbers the square root lies between.
1) √3
2) √7
4) −√50
3) √111
5) −√27
Compare: Use >, <, ≤, ≥, or =
6) 12
√12
7) √169
13
10) Part A: Put in order least to greatest
8) -10
-√81
9) √27
Part B: Place the original numbers on the number line:
√9, √5, 2, 1.2, √24 , √125
0
1
2
3
4
5
√12
Try These:
Find the two consecutive integers the square root lies between.
1) √29
3) −√15
2) √110
4) −√72
Compare: Use >, <, ≤, ≥, or =
5) 16
√16
6) √121
11
8) √8
√45
10) √125 , √8, −√100 ,
-√201
7) -16
-√225
Order from least to greatest
9) √2 , 5.85, 42, −√33
11) Which of the following is the best estimate for √58 ?
A) 2.9
B) 7.7
C) 7.6
D) 5.8
12) Place the following numbers on the number line:
√2,
0
1
√18,
2
0.5,
√4,
3
√11
4
5
Classwork
1) Between which two whole numbers does √89?
A.
B.
C.
D.
2) Between what two consecutive whole
numbers is √75?
between 4 and 5
between 7 and 8
between 8 and 9
between 9 and 10
A.
B.
C.
D.
5 and 6
6 and 7
7 and 8
8 and 9
3) Which radical when rounded to the nearest tenth is closest in value to 8?
A. √45
B. √55
C. √65
D. √75
4) Between which two consecutive whole numbers is √150? Explain how you find your answer.
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Compare using <, >, ≤, ≥
5) 0.5
√1
6) √36
5
7) -3
-√9
8) √9
Write in order from least to greatest:
Write in order from greatest to least:
9) -3, 4, √36 , − √8 ,
10) 5.25, √144,
3.5, √5
-√49, √1, − √27,
11) Place the following on the number line below: 0, 1.5, -2, √9, √64, - √25,
-√16
√64
-1, 3
Compare and Order Real Numbers
Method 1
Method 2
1. Convert all numbers to decimals
(all to the same place)
2. Compare or Order
, ,
1. Convert all numbers to fractions
(must have a common denominator)
2. Compare or Order
, ,
,0.5,0.7
,0.5,0.7
Examples: Compare: Use >, <, ≤, ≥, or =
1) 0.60.525
2)
√9.61
6)
5)
3) - 0.8
√456.685
-
4)
7) 3 + √7
3
3.625
6
Order the given set of numbers from least to greatest:
8)
, , −
Try These:
,0.25,0.9
9)
, − , 1
, 1.25, −1.1, √8 , −√4
1) 0.250.2
5) 0. 70.7
2)
−
4
7
−
5
9
3)
7) −2
6) −0.75 − 0.7
4) −4
0.5
5
8
−3.6
7
8
8) 6
Order the given set of numbers from least to greatest:
9)
, , −
, 0. 6, 0.6
11) Plot √6 on the number line below
10)
,√4,
Plot the given set of numbers on the number line:
12)
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
, − , −
, , 2
, √9,
3.9
√240