NEW
Font size
S
M
L
XL
WorksheetsSquare Roots and the Pythagorean Theorem Review
Total questions: 65
Worksheet time: 1hrs 5mins
Name
Class
Date
1.
The period T of a pendulum is the time, in seconds, it takes the pendulum to swing back and forth. The period can be found using the formula T = 1.1√L, where L is the length, in feet, of the pendulum. A pendulum has a length of 4 feet. Find its period.
a)
5.1 seconds
b)
4.4 seconds
c)
3.1 seconds
d)
2.2 seconds
2.
What is the value of x in the right triangle shown?
a)
16cm
b)
18cm
c)
24cm
d)
√674cm
3.
Find the height of the tree in the diagram.
a)
22.5ft
b)
31.5ft
c)
35ft
d)
40ft
4.
Which expression is equivalent to 12√24?
a)
48√6
b)
24√12
c)
24√6
d)
6
5.
An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?
a)
65 miles
b)
89 miles
c)
45.4 miles
d)
We don't have enough information.
6.
what is the formula for finding the hypotnuse?
a)
a2+b2=c2
b)
a+b=c
c)
a-b=c
d)
c-a=c
7.
What is the length of x?
a)
5
b)
7
c)
8
d)
25
8.
The legs of a right triangle form what type of angle?
a)
Acute
b)
Obtuse
c)
Reflex
d)
Right
9.
What is the opposite of squaring a number?
a)
divide
b)
multiply
c)
fractions
d)
square root
10.
The pythagorean Theorem ONLY works on which triangle?
a)
obtuse
b)
scalene
c)
isosceles
d)
right
11.
Find the length of the missing side.
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
12.
Find the length of the missing side.
a)
20 in.
b)
68 in.
c)
16 in.
d)
80 in.
13.
What is the longest side of a right triangle called?
a)
Leg A
b)
Leg B
c)
Hypotenuse
d)
Pythagoras' Big Buddy
14.
Determine if it is a rational or irrational number:
√20
√20
a)
Rational
b)
Irrational
15.
Determine if it is a rational or irrational number:
√101
√101
a)
Rational
b)
Irrational
16.
Every repeating decimal is a rational number.
a)
True
b)
False
17.
Give the approximate value of: √110
a)
10
b)
11
c)
100
d)
121
18.
Give the approximate: √48
a)
6
b)
7
c)
49
d)
36
19.
Which statement is true?
a)
All integers are rational numbers.
b)
Every integer is a whole number.
c)
Every terminating decimal is an irrational number.
d)
Some natural numbers are negative numbers.
20.
What number below is a natural, whole, integer, rational, and real number ?
a)
-4
b)
5.1
c)
0.7
d)
3
21.
Simplify √40
a)
4√10
b)
10√4
c)
2√10
d)
10√2
22.
What is √8 in simplest form?
a)
√8
b)
2√2
c)
2.82...
d)
(√7)×8%
23.
Simplify ∛343.
a)
7
b)
±7
c)
-7
24.
a)
A
b)
B
c)
C
d)
D
25.
Simplify the square root.
a)
A
b)
B
c)
C
d)
D
26.
a)
A
b)
B
c)
C
d)
D
27.
Simplify
a)
9
b)
√9
c)
3√9
d)
can't simplify
28.
Simplify
a)
2√6
b)
4√6
c)
12
d)
Can't Simplify
29.
Simplify
a)
100√6
b)
6√100
c)
10√6
d)
Can't Simplify
30.
Which of the following best defines rational numbers?
a)
numbers that can be written as a fraction or decimal that either terminates or continues forever in a repeating pattern
b)
numbers that make sense
c)
numbers that go on forever and ever with out a repeating pattern
d)
numbers cannot be written as a fraction
31.
Which answer is 1/4 in decimal form?
a)
0.4
b)
0.1
c)
1.4
d)
0.25
32.
Which answer is 3/5 in decimal form?
a)
3.5
b)
0.6
c)
.35
d)
.15
33.
In between what two integers is √77?
a)
5 and 6
b)
6 and 7
c)
7 and 8
d)
8 and 9
34.
In between what two integers is √44?
a)
3 and 4
b)
4 and 5
c)
5 and 6
d)
6 and 7
35.
Which of the following best defines irrational numbers?
a)
numbers that can be written as a fraction or decimal that either terminates or continues forever in a repeating pattern
b)
numbers that make sense
c)
numbers that go on forever and ever with out a repeating pattern and cannot be written as a fraction
d)
fractions
36.
What is the square root of 144?
a)
4
b)
12
c)
16
d)
32
37.
Approximate to the Nearest Tenths: √7
a)
3.5
b)
2.6
c)
2.7
d)
14
38.
Approximate to the Nearest Hundredth: √13
a)
5.66
b)
2.65
c)
3.97
d)
3.61
39.
Which number is NOT a perfect square?
a)
196
b)
169
c)
121
d)
132
40.
What is √25?
a)
625
b)
4.9
c)
5
d)
12.5
41.
Find the length of the missing side.
a)
17 cm
b)
22 cm
c)
15 cm
d)
13 cm
42.
Find the length of the missing side.
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
43.
Find the length of the missing side.
a)
20 in.
b)
68 in.
c)
16 in.
d)
80 in.
44.
Find the missing side.
a)
48
b)
108
c)
83.6
d)
72
45.
Find the missing side
a)
9
b)
41
c)
6.4
d)
3
46.
Which set of sides would make a right triangle?
a)
4,5,6
b)
8,10,12
c)
5,12,13
d)
5,10,12
47.
Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?
a)
17 miles
b)
32 miles
c)
37 miles
d)
40 miles
48.
You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?
a)
25 feet
b)
26 feet
c)
27 feet
d)
28 feet
49.
A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?
a)
111.8 yards
b)
115 yards
c)
127.3 yards
d)
119 yards
50.
a)
9.2 in
b)
11 in
c)
13 in
d)
9.6 in
51.
What is the distance between the two points?
a)
6.3
b)
6.5
c)
6.7
d)
16
52.
Find the distance.
a)
7.1
b)
7.8
c)
8.7
d)
8.9
53.
Side a on a right triangle is ALWAYS the longest side.
a)
true
b)
false
54.
you ADD a2 and c2 then take the square root to find b on a right triangle.
a)
true
b)
false
55.
The Pythagorean Theorem is
a2 + b2 + c2
a2 + b2 + c2
a)
false
b)
true
56.
The Pythagorean Theorem is
a2 + b3 = c4
a2 + b3 = c4
a)
false
b)
true
57.
The LEGS form what type of angle?
a)
Acute
b)
Obtuse
c)
Reflex
d)
Right
58.
To use the Pythagorean Theorem, the triangle MUST be what kind of triangle?
a)
obtuse
b)
scalene
c)
isosceles
d)
right
59.
What is the opposite of squaring a number?
a)
dividing it
b)
multiplying it
c)
using fractions
d)
taking the square root
60.
Is this a right triangle?
a)
Yes
b)
No
61.
Is this a right triangle?
a)
Yes
b)
No
62.
Is this a right triangle?
a)
Yes
b)
No
63.
Is this a right triangle?
a)
Yes
b)
No
64.
Is this a right triangle?
a)
Yes
b)
No
65.
What is the longest side of a right triangle called?
a)
Leg A
b)
Leg B
c)
Hypotenuse
d)
Pythagoras' Big Buddy
Reset
