Lesson 2
RCSD Geometry Local Curriculum
Name:__________________________
U1
Period:_______ Date:____________
Lesson 2: Classifying Real Numbers
Learning Targets :
 I can identify rational and irrational number
 I can use the properties of rational and irrational numbers
New Concepts /Vocabulary
Perfect Square: A ________________ multiplied by ____________________.
Example
Rational Numbers: A value that can be expressed as a __________________ of two integers
Example
(terminating and repeating decimals only)
Irrational Numbers: A value that ____________ be expressed as a _____________ of two integers
Example :
(non-ending, non-repeating decimals)
Finding perfect squares: Complete the table.
12
22
32
1
4
9
To take the square root of a number means to find a value that when __________________ by itself gives
you the ___________________ number. Not all the numbers are perfect square.
At this level of algebra and geometry, we only find the square roots of _______________ numbers.
**In Algebra II, we will see that the square root of a negative number is an_____________________ number.
What happens if we try find the square root of non- perfect squares? Will your answer be a rational or an irrational
number ? Justify you answer
Lesson 2
RCSD Geometry Local Curriculum
Name:__________________________
U1
Period:_______ Date:____________
On you own:
Example 1. State if the following are rational (R) or irrational (I). If it is irrational, give a decimal approximation
to the nearest hundredth.
1
3
1. 23
2. 4.581
3. 0
4. 
5.
169
6. 2.151515…
7. 14
8. 3.121221222…
9.
1
9
10.
11.  225
12.
1
8
50
Operations with rational numbers
Add any two rational number
Multiply any two rational numbers
Adding two rational numbers is the same as adding two fractions, which will result in another fraction. Thus,
adding two rational numbers produces another rational number.
Conclusion: The sum of two rational numbers will be a rational number
Multiplying two rational numbers is the same as multiplying two fractions, (all rational numbers can be
expressed as a fraction) the result in another fraction
Conclusion: The product of two rational numbers will be a rational number
Operations with Irrational numbers
Add the following Irrational Numbers
Multiply the following Irrational Numbers
2√3 + √2 =
√8 ∙ √3 =
2 + 3√7 + (−3 √7) =
√8 ∙ √2 =
Conclusion: The sum of two irrational numbers is ___________________ an irrational number
Conclusion: The product of two irrational numbers is ___________________ an irrational number
Lesson 2
RCSD Geometry Local Curriculum
Name:__________________________
U1
Period:_______ Date:____________
Operations with a mix of Rational and Irrational numbers
Add the following Irrational Numbers
3 + √2 =
1
5
+𝜋 =
Multiply the following Irrational Numbers
1
3
∙ √3 =
0 ∙ √2 =
Conclusion:
The sum of a rational and irrational number is ______________ an irrational number
The product of a rational and an irrational numbers is ______________ an irrational number
The product of a non -zero rational and an irrational number is ____________ an irrational number
Example 2
Determine whether each statement is true or false. Justify your answer by providing an example.
a) The sum of two rational numbers is rational
b) The sum of a rational number and irrational number is rational.
c) The product of a nonzero rational number and an irrational number is irrational.
Lesson 2
RCSD Geometry Local Curriculum
Name:__________________________
U1
Period:_______ Date:____________
Lesson 2: Classifying Real Numbers
Classwork
1. Determine whether each number is rational (R) or irrational (I)
a. √100 _____________________________________________________
b. √15 _____________________________________________________
c.
4
9
d. 0
_____________________________________________________
_____________________________________________________
e. –10.46 __________________________________________________
f. –11
g. 𝜋
h.
21
3
_____________________________________________________
______________________________________________________
______________________________________________________
2. Determine whether each statement is true or false. Justify your answer by providing an example.
a. The sum of two rational numbers is irrational
b. The sum of a rational number and irrational number is irrational.
c. The product of two irrational numbers is always an irrational number.