Review of Unit 2-Square Roots & Exponents 1. Do you agree or disagree with the following statement? “All radical expressions are irrational.” Why or why not? 2. Label and describe the parts of a right triangle. 3. How do you know when to label a number as rational or irrational? 4. When and why do we use scientific notation? 5. Estimate the roots below and graph the solution on the number line. Remember to place the point on the line and put numbers and spaces on the line. A. The square root of 81 B. The square root of 113 C. The negative square root of 400 6. What is the number of hours in I month (30 days) expressed in scientific notation? 7. Simplify and rewrite with positive exponents. 18 x −3 y −1 −3 2 −1 a. 6a b z b. 6 x −2 8. Simplify: a. 3 + 5 + 5
9.
b. 2 6 − 3 8
c. 3 5 ⋅ 2 6
d.
3 2 6
If a ladder is 20 meters long and it extends 10 meters from the base of the house. How high is the house?
10. If the area of a square is 25 ft 2 , what is the length of one of the sides?
11. To the nearest meter, how long is the diagonal of a 16 meter by 20 meter wall? 12. Solve:
625
13. In the diagram below, ∆ABD is a right triangle. The leg measurements are 6m and 8m. What is the measure of side c? A
c B
D
14. Kyle is siding his house using a chevron pattern (right triangles). If the longest board is 225 what could be the length of the shortest boards. 15. Estimate the positive square root of:
139
16. What are the solutions of y 2 = 49? 17. Evaluate 3( n −5) when n=1 ? 18. A deadly microbe is 2.34 x 10−4 inches. What is the standard form of this number? 19. What is the product of 50,000 and 20 written in scientific notation? 20. Which number will make the following statement true? 35 ÷ 33 = 32 ⋅ 3W 21. Simplify:
6⋅ 3+
22. Simplify
12 ⋅ 15
2 3
23. Simplify: 2-2(23) 24. Evaluate the exponential expression, and write your answer as a fraction in 1 simplest form: ( )-3 4
Answers to Review !. Radical expressions that are perfect squares are rational. Radical expressions that are not perfect squares are irrational. 2.A right triangle consists of 2 legs and a hypotenuse. The hypotenuse is always opposite the right angle. The legs form the right angle. 3.special numbers such as pi and the square root of a number that is not a perfect square are irrationals. All other numbers can be written in the form of a/ b and are rational numbers. 4.Scientific notation is used to write very large numbers and very small numbers. It is used for ease in reading and writing these numbers as well as ease in displaying and calculating with these large numbers on a calculator where the display will only hold a limited number of characters. 5.
A. 9. Graph on number line between 8 and 10 B. irrational number but estimates between 10 and 11 slightly closer to 11 on the number line. C. Square root of 400 is 20. The negative of that being -20. Graph on the number line between -19 and -21.
6. 24 hours in one day, 30 days in one month-= 720 hours. notation 7.2 x 10 3. 7. a. b.
6b 2 a 3 z1
8. a.
3+2 5
9. a2+ b2 = c2
In Scientific
3x 2 3 = 3 x y xy
b. 2 6 − 6 2 a2 + 102 = 202
c. 6 30
d.
2 4
a2 + 100 = 400
a2 = 300
a= 10 3
10. 5 feet 11.a2+ b2 = c2 12. 25
162 + 202 = c2
256 + 400 = c2
656 =c2
c= 4 41
13. a2+ b2 = c2
62 + 82 = c2
36+64= c2
c2 = 100
14. a2+ b2 = c2 15
a2+ b2= 225
(think Pythagorean triples) a= 9; b=12; and c=
15. between 11 and 12, but closer to 12. 16. y = 7 and -7 17.
3−4 =
1 1 = 34 81
18. .000234 19. 1 x 106 20. 0
6 6 =3 2+ 3 3
21.
18 +
22.
3⋅ 4 ⋅3⋅5 = 3⋅ 2 5 = 6 5
23. (
1 1 )(23 ) = ⋅ 8 = 2 2 2 4
1 1 43 = 1 ÷ 3 = 1⋅ = 43 = 64 24. (Use reciprocals) 1 4 1 ( )3 4
c= 10