Download Page 2.7 Find Square Roots and Compare Real Numbers Goal

2.7 Find Square Roots and Compare Real Numbers
Goal • Find square roots and compare real numbers.
Warm-up: Record the definition and show an example for each of the following vocabulary words:
square root
radical
radicand
perfect square
SQUARE ROOT OF A NUMBER
Words
If b 2 = a, then ____ is a square root of ____.
Numbers
52 = 25 and (−5)2 = 25, so ____ and ____ are square roots of 25.
Example 1-Find square roots
Evaluate the expression.
a. − 36 = ____
The negative square root of 36 is ________.
All positive real numbers have two square roots, a positive and a negative square root.
The positive square root is called the principal square root.
b. 16
= ____
c. ± 64 = ____
The positive square root of 16 is ____.
The positive and negative square roots of 64 are ____
and ____.
Now YOU try it. Evaluate the expression.
1.
100
Page
3. ± 256
1
2. − 1
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. This means that s is the positive square root of 945. You can
use a table determine if 945 is a perfect square.
Number
Square of a Number
As shown in the table, 945 is _______________________________________. The greatest perfect
square less than 945 is ________. The least perfect square greater than 945 is _________.
The side length of the tabletop is about _____ inches.
Now YOU try it.
4.
32
5.
103
Approximate the square root to the nearest integer:
6. - 48
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:
Number
Real
Number?
Rational
Number?
144 , − 49, 32.
Irrational
Number?
Integer?
Whole
Number?
144
− 49
32
Example 4 - Graph and order real numbers
Order the numbers from least to greatest:
4
Graph the numbers on a number line using approximation.
, − 5, 13, −2.5, 9
3
Page
2
Read the numbers from left to right:
Now YOU try it.
7. Tell whether each of the following numbers is a real number, rational number, irrational
number, integer, or whole number and order the numbers from least to greatest by putting
them on the number line.
Number Real number?
Rational
number?
Irrational
number?
Integer?
Whole
number?
− 20
−
9
2
0
7
4.1
Page
3
5.2