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Math 8
Unit 2-Square Roots & Exponents
Study Guide
Name____KEY________
Date____________________
Period___________________
I. Knowledge and Understanding
1. State whether you agree or disagree with this statement and explain why:
“All decimal expressions are irrational.”
Disagree, Only decimals that are non-repeating and non-terminating are
irrational. Example:  = 3.14… is irrational, 2.6 is rational
2. How can you tell if a number is rational or irrational number?
Another way you can tell if a number is rational or irrational is if perfect square
is under a radical sign it is rational, if a non-perfect square is under a radical
sign it is irrational.
3. Why would you want to use scientific notation? You would want to use
scientific notation if the numbers you are using are very small or very large
and they contain too many zeros to easily count.
Proficiency of Skills
4 - 6:Answer each of the following expressions with an estimate or value and
then graph on a number line:
8
8.2
9
4. The square root of 67
√64 √67
√81
11
11.6
12
√121
√130
√144
5. The square root of 130
6. The negative square root
of 225 = - 15
-16
-15
7. What is the number of seconds in 9 days expressed in scientific notation?
9 days • 24 hours • 60 min • 60 sec = 777600 = 7.776 x 105
8 – 10: Simplify:
8. 5 + 2 + 5
2√5 + √2
9. 5 3 - 9 3
-4√3
8
10. 6
√48 = 4√3
-14
11 – 12: Simplify and rewrite with positive exponents.
11. 3x y z = 3 z
4
5
6
15c 6 d 3
12.
3c 4
6
= 5
x4 y5
c2 d3
13. If the area of a square is 121 ft 2 , what is the length of one of the sides?
The square root of 121 = 11, so the length of one side is 11 ft.
14. Solve:
529 = 23
15. Estimate the positive square root of:
230 is between √225 = 15 and √256
=16, closer to √225 so a good guess would be 15.2
16. What are the solutions of y 2 = 25? 5
17. What is 4(n 6) when n = 2 ? 4(2-6) = 4(-4) = (1/4)4 = 1/256
18. A mechanic measured the gap in a spark plug and found it to be 6.7 x 10 4
inches. What is the standard form of 6.7 x 10 4 ?
.00067
19. What is the product of 30,000 and 52 written in scientific notation?
1,560,000 = 1.56 x 106
20. Which number will make the following statement true?
57  55  52 5
A. 
= 5 2 > 53
B. =
C. >
D. <
21 – 24: Evaluate the following:
21. (9)0 =1
22.
196 =14
23. 33 = (1/3)3 = 1/27
24. 75  75 = 1
25. Simplify: 2-5(27) = 22 = 4
26. Evaluate the exponential expression, and write your answer as a fraction in
simplest form:
( ¼ )-2 = (4)2 = 16