Study Guide 8.2, 7.3, 8.5
8.2 Subsets of real number system. (Drag and Drop)
IXL: A8, D1
All numbers are rational or irrational.
1. What number is an irrational number?
a.
b.
c.
d.
√36
-4
.45
√2
2. What subset does the following belong
(-3, -2, -1, 0, 1, 2, 3)
a. Whole
b. Natural
c. Integer
d. Irrational
3. Which number is not a rational number
a. √15
b. √9
c. √25
d. -1/2
sum or product of two rational numbers is rational
sum of a rational number and an irrational number is irrational
product of a nonzero rational number and an irrational number is irrational.†
4. What subset does the following belong 3√5
5. What subset does the following belong 3√25
6. What subset does the following belong 3 + √25
7. What subset does the following belong 3 + √5
Absolute Value
1. |−.325| =
2. |−5| =
3. −|7| =
4. |−3/4| =
5. |−5 + −9| =
6. |9| =
7. What number is equivalent to |–5 | - |9|?
8. What number is equivalent to -|.125|
9. What value is equivalent to -|
−𝟏𝟎𝟎
−𝟐𝟓
10.
What value is equivalent to - |
11.
What value is equivalent to - |
12.
What value is equivalent to −
|
𝟏𝟎𝟎
−𝟐𝟓
𝟏𝟎𝟎
𝟐𝟓
𝟏𝟎𝟎
𝟐𝟓
|
|
Number line for Integers and Absolute Value
Integers
(add, subtract, multiply, and divide integers)
IXL: C 1, 3, 4





E1 – E9
temperature changes (above/below zero)
stock market (rose/dropped)
elevator, speed up/down
balance in a checking account (deposits/withdrawals)
changes in altitude (above/below sea level)
1. The highest temperature ever recorded at the top of Mt. Clare was 54° and
the lowest temperature was –31°. What is the difference in these two
temperatures?
2. During one week, the stock market did the following: Monday rose 18 points,
Tuesday rose 31 points, Wednesday dropped 5 points, Thursday rose 27
points and Friday dropped 38 points. If it started out at 1,196 on Monday, what did it
end up on Friday?
3. If the value of a stock went down $4.00 each week for a period of 6 weeks,
what is the value of the stock at the end of the 6 week period?
4. A submarine is 40 feet below the surface of the water. The sub rises 33 feet,
goes down 7 feet and finally rises another 17 feet.
5. Ace has $325.00 in his checking account at the beginning of the month. He
deposits $725.00 into his account. He withdraws 75.00 the first week, and
writes a check to pays his cell phone $92.00. What is the remaining amount in
his account?
8.5 Perfect Squares
IXL: F 13, 14
two consecutive whole numbers between which a square root lies.
IXL: F 15, 19
 A perfect square is a whole number whose square root is an
integer (e.g., The square root of 25 is 5 and -5; thus, 25 is a perfect
square).
 The square root of a whole number that is not a perfect square is
an irrational number (e.g., 2 is an irrational number). An irrational
number cannot be expressed exactly as a ratio.
The area determines the perfect square number.
If it is not a perfect square, the area provides a means for
estimation.
(Use the symbol to ask for the positive root and
for the negative root.)
Identify each perfect square.
100
8
0
9
1
25

when asking
6.5 positive exponents and perfect squares
IXL: E 1, 2, 3, 9
104 = 10,000
103 = 1000
102 = 100
101 = 10
10 0 =1.
If 10 is the base, the exponent will be the number of zeros.
20 = 1
50 = 1
0 0 = Undefined
1. Which exponential expression is equivalent to 8 x 8 x 8 x 8?
2. What does 100 equal?
3. The numbers 1, 4, 9, and 16 are called “perfect squares”
Find the next three numbers in the sequence.
4. 92
5. 24
6. 52
7. 33
8. Which is a model of 4²?
9. Draw a model representing 52
Find the two consecutive whole numbers between which a square root lies.
1. √72 ____________________
2. √10 ____________________
3. √23 _____________________
4. √52 _____________________