6 Mid-Chapter Quiz
Do you know HOW?
Find all the real square roots of each number.
- 100
- 0.49
Simplify each radical expression. Use absolute value symbols when needed.
-
36
x
2
square root of 36 , x squared end root
-
0.008
y
3
x
6
3
cube root of 0.008 , y cubed , x to the sixth end root ,
Simplify.
-
50
x
4
y
8
square root of 50 , x to the fourth , y to the eighth end root
-
32
m
7
n
9
4
the fourth , root of 32 , m to the seventh , n to the ninth end root ,
Multiply and simplify.
-
6
4
x
2
⋅
2
9
x
2
y
2
6 , square root of 4 , x squared end root , dot 2 . square root of 9 , x squared , y squared end root
-
9
3
⋅
9
3
cube root of 9 , , dot , cube root of 9 ,
-
16
x
8
4
⋅
x
14
4
the fourth , root of 16 , x to the eighth end root , . dot , the fourth , root of x to the fourteenth end root ,
Divide and simplify.
-
36
x
4
9
x
6
fraction square root of 36 , x to the fourth end root , over square root of 9 , x to the sixth end root end fraction
-
64
x
9
y
3
3
8
x
3
3
fraction cube root of 64 , x to the ninth , y cubed end root , , over cube root of 8 , x cubed end root , end fraction
Simplify. Rationalize all denominators.
-
10
81
3
−
8
24
3
10 , cube root of 81 , , minus 8 , cube root of 24 ,
-
4
+
12
4
−
12
fraction 4 plus square root of 12 , over 4 minus square root of 12 end fraction
-
48
−
3
27
+
2
75
square root of 48 minus 3 square root of 27 plus 2 square root of 75
-
(
3
+
63
)
(
1
+
7
)
open , 3 plus square root of 63 , close . open , 1 plus square root of 7 , close
-
x
6
y
3
fraction square root of x , over square root of 6 , y cubed end root end fraction
Write each expression in exponential form.
-
−
17
negative square root of 17
-
y
8
3
cube root of y to the eighth end root ,
Write each expression in radical form.
-
m
3
7
m super 3 sevenths end super
-
y
−
4
3
y super negative , 4 thirds end super
Simplify each expression.
-
(
−
27
)
2
3
open , negative 27 , close super 2 thirds end super
-
(
16
)
3
4
open 16 close super 3 fourths end super
Write each expression in simplest form.
-
7
2
x
3
−
3
2
x
3
7 , cube root of 2 x end root , , minus 3 , cube root of 2 x end root ,
-
2
32
x
2
+
3
72
x
2
2 . square root of 32 , x squared end root . plus 3 . square root of 72 , x squared end root
-
125
x
6
3
−
27
x
6
3
cube root of 125 , x to the sixth end root , . minus . cube root of 27 , x to the sixth end root ,
-
7
4
−
7
3
the fourth , root of 7 , , minus , cube root of 7 ,
-
(
y
−
3
)
(
y
+
2
3
)
open , square root of y minus square root of 3 , close . open . square root of y plus 2 square root of 3 . close
-
(
16
x
1
4
y
3
4
)
−
4
open . 16 , x super 1 fourth end super . y super 3 fourths end super . close super negative 4 end super
-
(
x
1
3
y
2
3
)
9
open . fraction x super 1 third end super , over y super 2 thirds end super end fraction . close to the ninth
-
(
x
−
10
x
5
)
2
5
open . fraction x super negative 10 end super , over x to the fifth end fraction . close super 2 fifths end super
- The radius of a circle can be expressed as
r
=
A
π
r equals , square root of eh over pi end root inches where r is the radius and A is the area of the circle. If the area of a circle is
169
π
in
.
2
,
169 pi , in , . squared . comma what is its radius?
Do you UNDERSTAND?
- What are the real roots of
−
16
?
square root of negative 16 end root , question mark Explain.
-
Error Analysis Identify the error in this statement.
x
3
y
3
⋅
y
3
y
3
=
x
y
3
y
fraction cube root of x , , over cube root of y , end fraction . dot . fraction cube root of y , , over cube root of y , end fraction . equals . fraction cube root of x y end root , , over y end fraction
-
Reasoning If
0
2
3
=
0
,
0 super and 2 thirds end super , equals 0 comma why is
0
−
2
3
0 super negative , 2 thirds end super undefined?
- Given that x and y are integers, explain why the product of
x
+
y
x plus square root of y and its conjugate will always be an integer.
-
Reasoning Explain why
(
−
8
)
1
2
≠
−
(
8
)
1
2
,
open , negative 8 , close super 1 half end super . not equal to negative . open 8 close super 1 half end super . comma but
(
−
27
)
1
3
=
−
(
27
)
1
3
.
open , negative 27 , close super 1 third end super . equals negative . open 27 close super 1 third end super . .
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