Transcript lesson 2.7
2.7
Find Square Roots and Compare Real Numbers
Warm Up
Lesson Presentation
Lesson Quiz
2.7
Warm-Up
Find the square of the number.
1.
14
ANSWER 2.
16 196
4.
ANSWER Complete the statements using
<, >, or =
.
3.
– 2.5
?
– 19 8
ANSWER
< 5 6 ?
ANSWER
21 25 256 <
2.7
Warm-Up
5.
A square room has a side length of
25
feet. What is its area?
ANSWER
625
ft 2
2.7
Example 1
Evaluate the expression.
a.
36
=
6
b.
49
=
7
c.
–
4
= –
2
The positive and negative square roots of
36
are
6
and –
6
.
The positive square root of
49
is
7
.
The negative square root of
4
is –
2
.
2.7
Guided Practice
Evaluate the expression.
1.
–
9
= –
3
2. 3 .
25
=
5 64
=
8
4.
–
81
= –
9
2.7
Example 2
FURNITURE 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
that
s
2
=
945
.
This means that
s
of the tabletop such is the positive square root of
945
.
You can use a table to determine whether
945
is a perfect square
.
2.7
Example 2
As shown in the table
,
945
is not a perfect square
.
The greatest perfect square less than
945
perfect square greater than
945
is
961
.
is
900
.
The least
900
<
945
<
961 900
<
945
<
961 30
<
945 < 31
Write a compound inequality that compares
945
with both
900
and
961
.
Take positive square root of each number.
Find square root of each perfect square.
2.7
Example 2
Because
945
is closer to
961
than to
900
,
945
is closer to
31
than to
30
.
ANSWER The side length of the tabletop is about
31
inches
.
2.7
Guided Practice
Approximate the square root to the nearest integer.
5.
32 6
6.
103 10
7.
–
48
8.
–
350
–
7
–
19
2.7
Example 3
Tell whether each of the following numbers is a real number, a rational number, an irrational number, an
24 100 – 81
.
Number Real Number ?
24 100 – 81
Yes Yes Yes Rational Number ?
Irrational Number ?
Integer ?
Whole Number ?
No Yes Yes Yes No No No Yes Yes No Yes No
2.7
Guided Practice
9.
– 9 2
an irrational number, an integer, or a whole number.
ANSWER real number and rational number
2.7
Example 4
SOLUTION
3 13
Graph the numbers on a number line.
ANSWER
4 3 13 .
4 3 13
2.7
Guided Practice
10.
Copy and complete using < or >: (a)
– 5 ?
–2.5
ANSWER > (b)
7 ?
ANSWER <
14 5
2.7
Example 5
Rewrite the given conditional statement in if-then form. 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 an irrational number.
The statement is true
.
2.7
Example 5
b. Given: All real numbers are rational numbers
.
If-then form:
If a number is a real number, then it is a rational number.
number but not a rational number
.
2.7
Guided Practice
Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false
.
If it is false, give a counterexample
.
11.
All square roots of perfect squares are rational numbers. If-then form:
If a number is the square root of perfect square, then it is a rational number.
The statement is true
.
2.7
Guided Practice
Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false
.
If it is false, give a counterexample
.
12.
All repeating decimals are irrational numbers
.
If-then form:
If a number is a repeating decimal, then it is an irrational number.
The statement is false. For example, repeating decimal and can be written as , so it is a rational number
.
0.333… 3
is a
2.7
Guided Practice
Rewrite the given conditional statement in if-then form. Then tell whether the statement is true or false
.
If it is false, give a counterexample
.
13.
No integers are irrational numbers
.
If-then form:
If a number is an integer, then it is not an irrational number.
The statement is true
.
2.7
Lesson Quiz
Evaluate the expression.
1.
+ 289
ANSWER 2.
–
36
ANSWER
– 6
Approximate the square root to the nearest integer.
3
.
–
21
ANSWER
– 5
4
.
620
ANSWER
25
2.7
Lesson Quiz
5
.
A square courtyard has an area of 272 square feet. What is the side length of the courtyard to the nearest foot?
ANSWER
16 ft