Download QUIZ: Radicals

Name:
Period
11/28/11 -12/9/11
RIGHT TRIANGLES
I can define, identify and illustrate the following terms:
Square root
Rationalize
Like radicals
Special Right Triangles
Factors
Pythagorean Theoreom
Geometric Mean
Dates, assignments, and quizzes subject to change without advance notice.
Monday
28
Simplifying, ×, ÷
Radicals
5
Tuesday
29
Rationalizing the
denominator
6
Problem Solving
Quiz – Special Rights
12
GEOMETRIC MEAN
13
Review for Final
Block Day
30/1
Pythagorean Thm &
45°-45°-90° Triangles
Quiz - Radicals
7/8
REVIEW
14/15
Review for Final
Friday
2
30°-60°-90° Triangles
9
TEST 9
16
FINALS
FINALS
Monday, 11/28
Basic Radical Operations
I can simplify radicals.
I can multiply and divide radicals.
PRACTICE: Radical Worksheet #1
Tuesday, 11/29
Rationalizing Radicals
I can simplify radicals by rationalizing the denominator.
PRACTICE: Radical Worsksheet #2
Wednesday, 11/30 or Thursday, 12/1
Pythagorean Theorem and 45°-45°-90° Triangles
QUIZ: Radicals
I can use the Pythagorean theorem to solve for the missing side of a triangle, and leave my answer in
simplest radical form.
I can explain the difference between an exact answer and an approximate answer, and tell what situations
are best for each.
I know and can apply the 45°-45°-90° triangle pattern.
PRACTICE: 45°-45°-90° Worksheet
Friday, 12/2
30°-60°-90° Triangles
I know and can apply the 30°-60°-90° triangle pattern.
PRACTICE: 30°-60°-90° Worksheet
Monday, 12/5
Mixed Practice and Problem Solving
QUIZ: Speical Right Triangles
I can decide which pattern or theorem to use to solve a problem.
PRACTICE: Mixed Applications Worksheet
Tuesday, 12/6
Geometric Mean
I can solve problems using geometric means.
PRACTICE: Geometric Mean Worksheet
Wednesday, 12/7 and Thursday, 12/8
Review
PRACTICE: Review Worksheet
Friday, 12/6
Test: Special Right Triangles
I can demonstrate knowledge of ALL previously learned material.
Score:
Name:
Period:
Radical Operations: Simplifying, Multiplying, and Dividing
Review of Simplifying and Multiplication
To simplify 7 90 :
• First do a factor tree of 90
• Then find your pairs/perfect squares and
square root them to move them outside.
• Finally multiply all numbers inside the
radical together and all numbers outside
the radical together.
7 90
7 9*10
7 3*3*5* 2
3*3 = 9 and the
9 = 3.
7*3 5* 2
21 10
Simplify.
1.
18
5.
62
2.
6.
28
35
10. 16x 6 y 3 z 2
3. 3 27
7.
t2
11.
48r 2 s 7t
To multiply 3 7 * −4 3 :
• First simplify each separate radical if needed
• Then multiply all numbers inside the
radical together and all numbers outside
the radical together
• Finally simplify again if needed
8.
4. −5 108
r9
9. 12x 3
12. 2ab3 8a5b 2 c8
3*-4 7 *3
-12 21
Multiply. Simplify your answer.
13. (– 36 )2
14. – ( 9 )2
15. ( 14 )( 7 )
16. ( 6 )(– 30 )
11 * 11
17.
18. – 6 *
21. – (– 7 )2
25. – 11 *
22.
22
(
)(
7 *
26. (–
30 x 3 * 5 x
29.
)(
)
3
3
2 )(– 60 )
2
30.
32. 2 14 8 27 15 15
6
(
r 2 s5
)(
18st 3
27
3
20. – ( 9 )2
23. ( 14 )( 7 )
24. ( 6 )(– 30 )
27. –8 108 * 2 6
28. ( 54 )(– 20 )
)
36.
48
6
30 * 8 * 18
31.
(
)(
34. 24 x y 3 z 3 32 x 4 yz 2
33. x y * y z * z x
Review of Division
5 10
To divide
:
3 2
• First simplify each separate radical if needed
• Then if possible divide the radicands together
and the numbers outside the radical together.
• Finally if needed simplify again.
35.
19. (– 36 )2
10
or
2
same thing!!
Hint:
10
means the
2
5 5
3
37.
8 15
5 3
)
38.
11 55
11
Name:
Period:
Radical Operations: Rationalizing
Rationalize
You rationalize when there is a radical in the denominator of the fraction that does not simplify out on its
own (like yesterday’s division problems).
•
•
For
First try to simplify with division
Is there still a radical in the denominator? If so, multiply by 1 in its “clever form of 1”. This means to
create a fraction that is equivalent to one using that radical.
1
the “clever form of 1” is
5
Now we simplify and get
5.
1
17
5
1
5 1* 5
so our problem will look like
*
=
.
5
5
5
5*5
5
.
5
6.
11
11
7.
98
2
8.
7
11
Divide or rationalize. Simplify your answer.
9.
98
2
10.
48
6
11.
7
11
12.
2 11
3 5
13.
24
6
14.
1
28
15.
10
3 2
16.
96
54
17.
6
48
18.
21.
x3
x
2 x2
22.
6
25.
1
8xy 4
 2 6  10 
28. 



 5  8 3 
26.
8 15
5 2
ab
ac
19.
23.
27.
1
5
20.
12 x
24.
3x 2
3 15r 3 s 2t
5st
 2 x   y3

29. 
 y   10 x 5






17
85
12 y 5
28 x
Name:
Period:
45-45-90 Triangles
I. Complete the following table for the 45-45-90 triangles using exact simplified radical values.
Leg 1
Leg 2
Hypotenuse
8 2
Ratios
1.
3
2.
8 2
3.
5
4.
4 2
II. Fill in the length of each segment in the following figures.
5.
6.
7.
3 6
45˚
7
10 2
45˚
7.
8.
9.
45˚
40
5
45˚
4t
10.
11.
12.
9y
2x 5
45˚
2x 6
For 13 – 15, tell if the given values could be the sides of a 45°-45°-90° triangle.
13. 3 70 , 3 70 , 12 35
14.
10 , 10 , 2 5
15.
6,
6,
3
16. Sam has a square backyard divided into 2
sections along the 40 foot diagonal. One of
these sections is used as a garden. What is the
approximate area of the garden?
21. Find the value of x in simplest radical form.
17. A guy wire supporting a radio tower is
positioned 145 feet up the tower. It forms a 45˚
angle with the ground. About how long is the
wire?
22. Each edge of the cube
has length e.
45˚
a. Find the diagonal
length d if e = 1, e = 2,
and e = 3. Give the
answers in simplest
radical form.
23. Solve for the following. Leave answer in
simplest radical form.
18. Find the perimeter and area of a 45°-45°90° triangle with a hypotenuse length 12 inches.
Give your answers in simplest radical form.
3
x
6
15
19. Find the perimeter and area of a square with
diagonal length 18 meters. Give your answers
in simplest radical form.
9
x
14
28
20. This triangle loom is made from wood
strips shaped into a 45°-45°-90° triangle. Pegs
are placed every 1 inch along each leg.
2
Suppose you make a loom with an 18-inch
hypotenuse. Approximately how many pegs
will you need?
x
24. Given AC = 10, find BX in simplest
radical form.
B
10
A
X
C
Name:
Period:
30-60-90 Triangles
1. In a 30˚-60˚-90˚ triangle, the short leg is located across from what angle?
Complete the table for a 30˚-60˚-90˚ triangle using exact (radical) values.
Short Leg
Long Leg
Hypotenuse
Ratios
2.
5
3.
14
4.
6 3
5.
2 3
6.
9
7.
10 y 3
8.
7ab 2
Fill in the blanks for the special right triangles.
9.
10.
11.
5 2
30°
30˚
20
60˚
12
12.
13.
14.
9t
2 33
30˚
4y
60˚
60°
15. ∆RJQ is equilateral.
16. ∆ABC is equilateral.
B
J
JQ =
4 3
AD =
RL =
DC =
h
LQ =
R
L
Q
JL =
AB =
A
D
C
BC =
For 17 – 20, tell if the given values could be the sides of a 30°-60°-90° triangle.
17. 2, 2 3 , 4
18. 9, 3, 3 3
21. The hypotenuse of a 30-60-90 triangle is
12 2 ft. Find the area of the triangle.
19.
3 , 3,
20. 4 6 , 2 6 , 6 2
6
27. Find QR and PS. Answer in simplest
radical form.
P
50
22. Find the perimeter and area of a 30°-60°90° triangle with hypotenuse length 28
centimeters.
Q
R
S
23. Find the perimeter and area of an equilateral
triangle with side length 4 feet.
28. Solve for the following. Leave answer in
simplest radical form.
8
x
12
24. Find the perimeter and area of an equilateral
triangle with height 30 yards.
16
8
x
25. A skate board ramp must be set up to rise
from the ground at 30˚. If the height from the
ground to the platform is 8 feet, how far away
from the platform must the ramp be set?
9
x
6
8 ft
30˚
26. Find the value of x in simplest radical form.
29. The perimeter of a rectangle is 60 in. The
length is four times the width. What is the
length of the diagonal?
Name:
Period:
Mixed Applications
I. For each problem:
1) Determine if you should use Pythagorean Theorem, 30°-60°-90°, or 45°-45°-90°
2) Write the equation or pattern you will use
3) Show work and find all the missing segment lengths
1. Use: ____________________
O
5
Formula: ________________ 3
Work and Answer(s):
C
4
Formula: ________________
Work and Answer(s):
W
3. Use: ____________________
Formula: ________________
Work and Answer(s):
60°
2. Use: ____________________
4. Use: ____________________
5 3
30°
2p
Formula: ________________
Work and Answer(s):
R
5. Use: ____________________
P
6. Use: ____________________
10 2
Formula: ________________
Work and Answer(s):
5 3
Formula: ________________
Work and Answer(s):
Z
I
5
B
7. ∆ABC is equilateral with
perimeter 36y units. Find the
length of each side and the
height.
8. C is the center of a regular hexagon.
Find the length of each side.
Use: ____________________
A
Use: ____________________
Formula: ________________
Work and Answer(s):
D
C
C
Formula: ________________
Work and Answer(s):
30
6
Draw a picture if one is not given and solve the problem.
9. The four blades of a helicopter meet at right angles and are all the same length. The distance between
the tips of two adjacent blades is 36 ft. How long is each blade? Round your answer to the nearest tenth.
10. An escalator lifts people to the second floor, 25 ft. above the first floor. The escalator rises at a 30º
angle. How far does a person travel from the bottom to the top of the escalator?
11. A slide was installed at the local swimming pool, as shown here.
What is the length of the slide?
12. After heavy winds damaged a house, workers placed a 6 m. brace against its side at a 45° angle.
Then, at the same spot, they placed a second, longer brace to make a 30° angle with the side of the
house.
a. How far away from the house are the braces placed on the ground?
30°
b. How long is the longer brace?
45°
c. How much higher on the house does the longer brace reach than the shorter brace?
*13. Magic Plumbing is needing to ship out a new water pipe to replace a broken one in the Smith’s
house. The only box they could find has dimensions of 20 in x 16 in x 12in. The pipe they need to ship
is 24 inches long. Will it fit in the box? Explain your answer.
Right Triangles and Altitudes/ Geometric Mean
If ∆ABC is a right triangle and CD is the altitude to the hypotenuse AB then
m a
∆ABC ~ ∆CBD →
= →a² = mc
a
b
h
a c
n b
∆ABC ~ ∆ACD → = → b² = nc
m
n
b c
m h
∆ACD ~ ∆CBD → = → h² = mn
c
h n
1. c = 12; m = 6; a = ?
2. m = 4; h = 25; n = ?
3. c = 12; m = 4; h = ?
4. a = 30; c = 50; h = ?
5. h = 12; m = 9; b = ?
6. a = 24; m = 4; b = ?
7. b = 45; n = 5; a = ?
8. b = 8; m = 12; c =?
10. a = 7 5 ; h = 14; c = ?; n = ?
9. h = 14; c = 35; n = ?
11. a = 6 5 ; b = 3 5 ; m = ?; h = ?
Pythagorean Inequality Practice
A triangle has the side lengths given. Decide whether the triangle is acute, obtuse , right, or not a
triangle.
12. 10, 12, 16
13. 8, 13, 23
14. 1.5, 2, 2.5
15. 6, 8, 11
16. 2 6 , 12, 13
17. 5 2 , 6, 8
18. 7, 7 7 , 26
19. 9, 40, 41