Warm-Up
1.14
ANSWER
196
2.16
ANSWER
256
Find the square of the number.
<
ANSWER
Complete the statements using <, >, or =.
ANSWER
<
3. 2.5
–
–
19
8
?
4.
5
6
21
25
?
Example 1
a.
–
+
36
=
+
–
6
The positive and negative square
are 6 and – 6.
roots of 36
b.
49
=
7
The positive square root of 49 is 7.
c.
4
–
=
2
–
The negative square root of 4 is – 2.
Evaluate the expression.
Example 2
FURNITURE
The top of a folding table is a square whose area is945 square inches. Approximate the side length of the
tabletop to the nearest inch.
SOLUTION
2
=
You need to find the side length s of the tabletop suchthat s 945. This means that s is the positive squareroot of 945. You can use a table to determine whether945 is a perfect square.
Example 2
As shown in the table, 945 is not a perfect square. Thegreatest perfect square less than 945 is 900. The leastperfect square greater than 945 is 961.
900 < 945 < 961
Write a compound inequality thatcompares 945 with both 900 and 961.
<
<
961
900
945
Take positive square root of eachnumber.
30
945
<
<
31
Find square root of each perfectsquare.
Example 2
Because 945 is closer to 961 than to 900, is closer to31 than to 30.
945
ANSWER
The side length of the tabletop is about 31 inches.
Guided Practice
Approximate the square root to the nearest integer.
5.
32
6
6.
103
10
7.
48
–
– 7
8.
350
–
– 19
Example 3
Tell whether each of the following numbers is a realnumber, a rational number, an irrational number, aninteger, or a whole number: , , – .
24
81
100
No
Yes
RealNumber?
WholeNumber?
Integer?
IrrationalNumber?
RationalNumber?
Number
24
100
–
81
Yes
No
No
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
No
Guided Practice
9.
Tell whether is a real number, a rational number,an irrational number, an integer, or a whole number.
9
2
–
ANSWER
real number and rational number
Example 4
Compare and .
4
3
13
SOLUTION
Graph the numbers on a number line.
Because is to the left of , < .
4
3
ANSWER
13
.
4
3
13
Example 5
Rewrite the given conditional statement in if-thenform. Then tell whether the statement is true or false.If it is false, give a counterexample.
SOLUTION
a.
Given: No fractions are irrational numbers.
If-then form: If a number is a fraction, then it is not anirrational number.
The statement is true.
Example 5
b.
Given: All real numbers are rational numbers.
The statement is false. For example, is a realnumber but not a rational number.
2
If-then form: If a number is a real number, then it isa rational number.
Guided Practice
Rewrite the given conditional statement in if-thenform. Then tell whether the statement is true or false.If it is false, give a counterexample.
All square roots of perfect squares are rational
numbers.
11.
If-then form: If a number is the square root of perfectsquare, then it is a rational number.
The statement is true.
Guided Practice
Rewrite the given conditional statement in if-thenform. Then tell whether the statement is true or false.If it is false, give a counterexample.
All repeating decimals are irrational numbers.
12.
If-then form: If a number is a repeating decimal, thenit is an irrational number.
The statement is false. For example, 0.333… is arepeating decimal and can be written as , so it isa rational number.
1
3
Guided Practice
Rewrite the given conditional statement in if-thenform. Then tell whether the statement is true or false.If it is false, give a counterexample.
No integers are irrational numbers.
13.
If-then form: If a number is an integer, then it is notan irrational number.
The statement is true.
Lesson Quiz
Evaluate the expression.
Approximate the square root to the nearest integer.
1.
–
+
289
ANSWER
–
+
17
2.
36
–
3.
21
–
ANSWER
– 5
ANSWER
– 6
4.
620
ANSWER
25