holt algebra 1 1-5 square roots and real numbers evaluate expressions containing square roots....
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Holt Algebra 1
1-5 Square Roots and Real Numbers
Evaluate expressions containing square roots.
Classify numbers within the real number system.
Objectives
Holt Algebra 1
1-5 Square Roots and Real Numbers
square root terminating decimalperfect square repeating decimalreal numbers irrational numbersnatural numberswhole numbersintegersrational numbers
Vocabulary
Holt Algebra 1
1-5 Square Roots and Real Numbers
A number that is _____________to form aproduct is called a square root of that product.The operations of squaring and finding a squareroot are _____________
The radical symbol , is used to represent square roots. Positive real numbers have twosquare roots.
4 4 = 42 = 16 = 4 Positive squareroot of 16
(–4)(–4) = (–4)2 = 16 = –4 Negative squareroot of 16
–
Holt Algebra 1
1-5 Square Roots and Real Numbers
A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table.
0
02
1
12
1004
22
9
32
16
42
25
52
36
62
49
72
64
82
81
92 102
The nonnegative square root is represented by . The negative square root is represented by – .
Holt Algebra 1
1-5 Square Roots and Real Numbers
The expression does not represent
a real number because there is no real
number that can be multiplied by itself to
form a product of –36.
Reading Math
Holt Algebra 1
1-5 Square Roots and Real Numbers
Example 1: Finding Square Roots of Perfect Squares
Find each square root.
42 = 16
32 = 9
Think: What number squared equals 16?
Positive square root positive 4.
Think: What is the opposite of the square root of 9?
Negative square root negative 3.
A.
= 4
B.
= –3
Holt Algebra 1
1-5 Square Roots and Real Numbers
Find the square root.
Think: What number squared equals ?25
81
Positive square root positive .59
Example 1C: Finding Square Roots of Perfect Squares
Holt Algebra 1
1-5 Square Roots and Real Numbers
Find the square root.
Check It Out! Example 1
Think: What number squaredequals 4?
Think: What is the opposite of the square root of 25?
1a.
1b.
.
Holt Algebra 1
1-5 Square Roots and Real Numbers
The square roots of many numbers like , are not whole numbers. A calculator can approximate the value of as 3.872983346... Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.
Holt Algebra 1
1-5 Square Roots and Real Numbers
Example 2: Problem-Solving Application
As part of her art project, Shonda willneed to make a square covered in glitter.Her tube of glitter covers 13 square inches. What is the greatest side lengthShonda’s square can have?
The answer will be the side length of the square.
List the important information:
• The tube of glitter can cover an area of 13 square inches.
Understand the problem11
Holt Algebra 1
1-5 Square Roots and Real Numbers
22 Make a Plan
The side length of the square is because
13. Because 13 is not a perfectsquare, is not a whole number. Estimate
to the nearest tenth.
=
Find the two whole numbers that isbetween. Because 13 is between the perfectsquares 0 and 16. is between and , or between 3 and 4.
Example 2 Continued
Holt Algebra 1
1-5 Square Roots and Real Numbers
3 4
Because 13 is closer to 16 than to 9, is closer to 4 than to 3.
You can use a guess-and-check method to estimate .
Example 2 Continued
Holt Algebra 1
1-5 Square Roots and Real Numbers
Guess 3.6: 3.62 = 12.96 too low Guess 3.7: 3.72 = 13.69 too high
is greater than 3.6.
is less than 3.7.
Solve33Example 2 Continued
3.6 3.7 43
Because 13 is closer to 12.96 than to
13.69, is closer to 3.6 than to 3.7. 3.6
Holt Algebra 1
1-5 Square Roots and Real Numbers
A square with a side length of 3.6 incheswould have an area of 12.96 square inches.Because 12.96 is close to 13, 3.6 inchesis a reasonable estimate.
Look Back44
Example 2 Continued
Holt Algebra 1
1-5 Square Roots and Real Numbers
All numbers that can be represented on a number line are called real numbers and can be classified according to their characteristics.
Holt Algebra 1
1-5 Square Roots and Real Numbers
Natural numbers are the counting numbers: 1, 2, 3, …
Whole numbers are the natural numbers and zero:
0, 1, 2, 3, …
Integers are whole numbers and their opposites: –3, –2, –1, 0, 1, 2, 3, …
Rational numbers can be expressed in the form ,
where a and b are both integers and b ≠ 0:
, , .
ab
12
71
910
Holt Algebra 1
1-5 Square Roots and Real Numbers
Terminating decimals are rational numbers in decimal form that have a finite number of digits: 1.5, 2.75, 4.0
Repeating decimals are rational numbers in decimal form that have a block of one or more digits that repeat continuously: 1.3, 0.6, 2.14
Irrational numbers cannot be expressed in the form . They include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat: , ,
ab
Holt Algebra 1
1-5 Square Roots and Real Numbers
Example 3: Classifying Real Numbers
Write all classifications that apply to each Real number.
A. –32
B. 5
Holt Algebra 1
1-5 Square Roots and Real Numbers
Write all classifications that apply to each real number.
3a. 7 49
3b. –12
Check It Out! Example 3
3c.
Holt Algebra 1
1-5 Square Roots and Real Numbers
Find each square root.
1. 2. 3. 4.
5. The area of a square piece of cloth is 68 in2. How long is each side of the piece of cloth? Round your answer to the nearest tenth of aninch.
Lesson Quiz
Write all classifications that apply to each real number.
6. 1
7. –3.89
8.