Chapter 7 Review
Name:_______________________ Period:____
SHOW YOUR WORK! It is GOOD practice for the test!
NO Calculators for problems 1 through 14. YOU WILL BE REQUIRED TO DO THESE ON THE TEST
WITHOUT A CALCULATOR SO PRACTICE WITHOUT YOUR CALCULATOR!
1. Find the square root or cube roots for perfect square and cubes. Know the ones from the sheet!
√25 √0.25 √27 1.
Evaluate the expression.
√0.36 2.5 √343 5 ∙ √64 + 10
√1000 10
1
81
3
3
1
∙ 2 ∙ √16 √25 2 ∙ √27 √81 3
169 5
5
3
3. The area of a cube is 64 cubic inches.
a. Write an equation that could be used to determine the length of one side of the cube.
b. How long is one side of the court? Show your work.
4. Estimate the square root to the nearest integer. Show your thinking!
√8 between which two integers?
√18 between which two integers?
√35 between which two integers?
√2.2 between which two integers?
√335 between which two integers?
√110 between which two integers?
5.
Determine whether each of the
numbers in the first column below
is rational or irrational and/or real.
Indicate your answers by placing a
correct box for each number.
Number
Rational
Irrational
6.
Determine whether each expression is
true or false. Indicate your answers by
placing a correct box for each
expression.
Real
Expression
√33 > 5.1
0
4π
2√2
√2
√. 49 > 0.7
9, "ℎ$% 3
7.1 < √49
5√3 < 5π
36
7
8
√15
Write the decimal as a fraction. Show your work!
Factor to find the roots. Show your work!
9. √720
> 9
5√2 < 3√5
20.455566...
7.
1
1
>
25
4
8.
10.
√3000
True
False
11. Name
the point on the number line associated with each irrational number.
12. Place an arrow on the number line for each of the following irrational numbers.
Label each arrow. Be PRECISE in your location placement!
13. Place an arrow on the number line for each of the following irrational numbers.
1
√12
Point A: √'(,)*+,-.:0 2 ,)*+,-3: √415,)*+,-6: 2 ,)*+,-7:18,)*+,-9:√:
Label each arrow. Be PRECISE in your location placement!
1
14.
2
3
4
5
6
'
7
YOU CAN USE YOUR CALCULATOR FOR THE REST OF THE REVIEW!
15. The area of square A is four times as much as the area of square B. The length of the side for
square B is 3 meters. What is the length of the side for square A? Explain your reasoning.
s=5m
B
A
16. Find the missing length of the triangle. Show your work.
17. Tell whether the triangle with the given side lengths is a right triangle. Show your work and explain
your reasoning.
A triangle has sides of 15 ft, 9 ft, and 12 ft.
A triangle has sides of 9 in., 11 in., √115 in.
A triangle has sides of 10 in., 16 in., 2√39 in.
18. ABCD is a quadrilateral composed of two right triangles where AD=3, and AB=AD+1, and DC=AD x
AB. Find AB, DC, BD, and BC.
.
.
19. Find the distance listed below.
a. How far is the cabin from the peak?
b. How far is the fire tower from the lake?
c. How far is the peak to the lake?
20. Find the perimeter of the trapezoidal brick to the nearest tenth of an inch.
8 inches
6 inches
12 inches
21)
22) All sides of a right triangle are integers. If the hypotenuse is 13 inches, find the lengths of the two
legs. Show your work.
23) A student made this conjecture (hypothesis or statement that he thinks is true) and found two examples to
support the conjecture (idea).
His statement or conjecture: If a rational number is not an integer, then the square root of that rational number
is irrational. For example, 2.1 is rational but the √2.1 is irrational. Provide two examples of non-integer rational
numbers that show that the conjecture is false.