Square Roots

1
Warm Up Simplify each expression. 1. 62

2. 112
121
36
25 36
3. (9)(9)
81
4.
Write each fraction as a decimal.
0.4
5.
6.
0.5
1.83
7.
8.
5.375
2
Roots and Irrational Numbers

• Section 1.5

3
Objectives

• In this lesson youll
• Evaluate expressions containing roots.
• Classify numbers within the real number system

4
Words to know

• Square root - a number which, when multiplied by
  itself, produces the given number. (Ex. 7² 49,
  7 is the square
• root of 49)
• Perfect square- any number that has an integer
  square root.(ex. 100 is a perfect square ,
• Cube root - a number that is raised to the third
  power to form a product is a cube root. (ex
  238, 2)

5
Square Roots

• Perfect Square Roots

• Squares
• 0² 0
• 1² 1
• 2² 4
• 3² 9
• 4² 16
• 5² 25
• 6² 36
• 7² 49
• 8² 64
• 9² 81
• 10² 100

6
Are squares and square roots inverses?
Start
Root it
Square it
Result
3
3
5
5
9
9
A square root is the inverse operation of a
square!
7
Do you know your perfect squares?
7 and -7
25
8 and -8
121
196
3 and -3
8
Square Roots

• Positive real numbers have two square roots.
• Find the square roots of 16.

Solution
Positive square root of 16
4
4 ? 4 42 16
(4)(4) (4)2 16
4
Negative square root of 16

The square roots of 16 are 4 and - 4.
9
Writing Math
Cube roots
10
You try
Find each root.
Think What number squared equals 81?
Think What number squared equals 25?
C.
Think What number cubed equals 216?
(6)(6)(6) 36(6) 216
6
(6)(6)(6) 36(6) 216
6
11
You try
Finding Roots of Fractions.
a.
b.
12
You try
Finding Roots of Fractions.
A.
B.
(6)(6)(6) 36(6) 216
6
13
Approximating Square Roots
14
Approximating Square Roots

• Approximate to the nearest whole number.

Solution
Is between 7² and 8².
15
Lets practice
Determine what two consecutive integers each root
lies between.
Between 2 and 3
Between 4 and 5
Between 4 and 5
Between 5 and 6
16
Words to know

• Natural numbers - The counting numbers.
  (example 1, 2, 3)
• Whole numbers - The natural numbers and
  zero.(example 0, 1,2,3)
• Integers -The whole numbers and their
  opposites.(ex -3,-2,-1,0,1,2,3)
• Rational numbers - Numbers that can be
  expressed as a fraction (a/b).

17
Words to know

• Terminating decimal -Rational numbers in decimal
  form that have finite (ends) number of digits.
  (ex 2/5 0.40 )
• Repeating decimal -rational numbers in decimal
  form that have a block for one or more digits
  that repeats continuously. (ex. 1.31.333333333)
• Irrational numbers - numbers that cannot be
  expressed as a fraction including square roots of
  whole numbers that are not perfect squares and
  nonterminating decimals that do not repeat.

18
The real numbers are made up of all rational and
irrational numbers.
19
Classifying Real Numbers
Write all classifications that apply to each
real number.
A.
32
32 1
32
32 can be written as a terminating decimal.
32 32.0
rational number, integer, terminating decimal
B.
irrational
20
Check It Out!
Write all classifications that apply to each real
number.
a. 7
rational number, repeating decimal
b. 12
12 can be written as a terminating decimal.
rational number, terminating decimal, integer
21
Write all classifications that apply to each real
number.
irrational
natural, rational, terminating decimal, whole,
integer
22
A challenge

• Would you know how to solve this.

-11
-11
x 5
23
A challenge

• Solve the variable.

-3
-3
x 8
24
Lesson Quiz
Find each square root.
4.
3.
5
1.
2.
3
1
5. The area of a square piece of cloth is 68 in2.
Estimate to the nearest tenth the side length of
the cloth.
? 8.2 in.
Write all classifications that apply to each real
number.
7.
rational, repeating decimal
irrational