Deck 8: Roots and Radicals

Question 1

Find the square root without using a calculator. $$\sqrt { 0.04 }$$

A)0.3
B)2
C)0.02
D)0.1
E)0.2

Answer 1

0.2

Question 2

Graph the function. $$f ( x ) = - 1 - \sqrt { x }$$

A)
B)
C)
D)
E)

Answer 2

Question 3

Use a calculator to find the root to the nearest hundredth. $$\sqrt [ 4 ] { 12,750 }$$

A)6.62
B)23.36
C)10.63

Answer 3

10.63

Question 4

Find the value. $$\sqrt [ 0 ] { - 1 }$$

A)-9
B)9
C) $- \frac { 1 } { 9 }$
D)- 1
E)1

Question 5

Find the cube root. Give the answer to the nearest hundredth. $$\sqrt [ 3 ] { - 22,155 }$$

A)28.09
B)29.32
C)- 27.53
D)- 29.32
E)-28.09

Question 6

Find the area of the isosceles triangle shown in the illustration, where a = 11 and b = 10.

A) $5 \sqrt { 96 } \mathrm { in } ^ { 2 }$
B) $55 \mathrm { in } ^ { 2 }$
C) $\sqrt { 96 } \mathrm { in } ^ { 2 }$
D) $10 \sqrt { 96 } \mathrm { in } ^ { 2 }$
E)none of the above

Question 7

Graph the function. $$f ( x ) = \sqrt [ 3 ] { x } + 2$$

A)
B)
C)
D)
E)

Question 8

Find the value without using a calculator. $$\sqrt [ 3 ] { - 729 }$$

A)-9
B)9
C)27
D)-27
E)not a real number

Question 9

Refer to the following illustration. Find $b$ if $a = 3$ and $c = 5$ .

A) $b = 8$
B) $b =$
C) $b = 4$
D) $b = 2$
E) $b = 5$

Question 10

Find the square root without using a calculator. $$\sqrt { 16 }$$

A)4
B)6
C) $-$ 4
D) $-$ 3
E)3

Question 11

Find the value without using a calculator. $$\sqrt [ 3 ] { 0.001 }$$

A)9
B)0.1
C)10
D)0.3
E)1

Question 12

Use a calculator to find the cube root to the nearest hundredth. $$\sqrt [ 3 ] { - 210 }$$

A) $-$ 5.94
B)14.46
C)5.94
D)14.49
E)none of the above

Question 13

A cubical box has a volume of 125 cubic feet. Substitute 125 for V in the formula $V = s ^ { 2 }$ , and solve for s to find the length of each side of the box.

A) $\frac { 5 } { 3 } \mathrm { cu } \mathrm { ft. }$
B)15 cu. ft.
C)10 cu. ft.
D)5 cu. ft.
E)none of the above

Question 14

The size of a television screen is the diagonal measure of its rectangular screen. How large is a screen if it is 16 inches wide and 20 inches high?

A)29 in.
B)28 in.
C)23 in.
D)25 in
E)22 in.

Question 15

A team of archaeologists travels 3.6 miles east and then 2.8 miles north of their base camp to explore some ancient ruins. "As the crow flies", how far from their base camp are they? Round to the nearest whole number.

A)6 mi
B)7 mi
C)15 mi
D)5 mi
E)4 mi

Question 16

The design for a set of brass pipes for a church organ are shown in the illustration below, where the red line is the graph of function . Find the length of each pipe (to the nearest tenth of a foot), and then find the total length of pipe needed to construct this set (to the nearest tenth of a foot). __________ ft

Question 17

This graph is

A) $f ( x ) = \sqrt [ 3 ] { x } + 1$
B) $f ( x ) = \sqrt [ 3 ] { x + 1 }$
C) $f ( x ) = \sqrt [ 3 ] { x }$
D) $f ( x ) = \sqrt [ 3 ] { x - 1 }$

Question 18

Find the cube root. Give the answer to the nearest hundredth. $$\sqrt [ 3 ] { - 0.11327 }$$

A)-0.48
B)0.42
C)0.48
D)-0.42
E)-0.44

Question 19

Graph the function. $$f ( x ) = - 5 + \sqrt { x }$$

A)
B)
C)
D)
E)

Question 20

Graph the function. $$f ( x ) = - \sqrt [ 3 ] { x } - 4$$

A)
B)
C)
D)
E)

Question 21

Simplify the expression. All variables represent positive numbers. $$\sqrt { \frac { 75 a ^ { 3 } b ^ { 3 } } { c ^ { 2 } d ^ { 6 } } }$$

A) $\frac { 5 a b \sqrt { 3 a } } { c d ^ { 5 } }$
B) $\frac { 5 a b \sqrt { 3 a } } { c d ^ { 3 } }$
C) $\frac { 5 a \sqrt { 3 a } } { d ^ { 3 } }$
D) $\frac { 6 a b \sqrt { 3 a } } { c d ^ { 5 } }$
E) $\frac { 6 a b \sqrt { 3 a } } { c d ^ { 3 } }$

Question 22

Use the product rule to simplify. $$\sqrt { 16 } \cdot \sqrt { 4 } \cdot \sqrt { 16 }$$

A)32
B)1024
C)4
D)2

Question 23

Use the product rule to simplify. $$\sqrt { 9 } \cdot \sqrt { 49 }$$

A)21
B)441
C)3
D)7

Question 24

Write the quotient as the quotient of two radicals and simplify. $$- \sqrt { \frac { 20 } { 49 } }$$

A) $- \frac { 2 \sqrt { 6 } } { 7 }$
B) $- \frac { 2 \sqrt { 5 } } { 7 }$
C) $- \frac { 3 \sqrt { 5 } } { 7 }$
D) $- \frac { 2 \sqrt { 5 } } { 8 }$
E)none of the above

Question 25

Find the value.

Question 26

Find the value without using a calculator. $$\sqrt [ 3 ] { 1,000 }$$

A)999
B)10
C)1,000
D)30
E)100

Question 27

Write the quotient as the quotient of two radicals and simplify. $$\sqrt { \frac { 121 } { 100 } }$$

A) $\frac { 5 } { 10 }$
B) $\frac { 10 } { 5 }$
C) $\frac { 11 } { 10 }$
D) $\frac { 10 } { 11 }$
E) $\frac { 121 } { 10 }$

Question 28

Rationalize the denominator and simplify. $$\frac { 5 } { \sqrt { 5 } + 1 }$$

A) $\frac { 5 ( \sqrt { 5 } - 1 ) } { 4 }$
B) $\frac { 5 \sqrt { 5 } - 1 } { 4 }$
C) $\frac { 4 ( \sqrt { 5 } - 1 ) } { 5 }$
D) $\frac { \sqrt { 5 } - 5 } { 4 }$
E) $5 ( \sqrt { 5 } - 1 )$

Question 29

Find the following product and express your answer in simplest radical form. $$\frac { \sqrt { 110 } } { 11 \sqrt { 10 } + 10 \sqrt { 11 } }$$

A) $\sqrt { 10 } - \sqrt { 11 }$
B) $\sqrt { 11 } - \sqrt { 10 }$
C) $\frac { \sqrt { 110 } } { \sqrt { 11 } + \sqrt { 10 } }$
D) $\sqrt { 11 } + \sqrt { 10 }$
E) $\frac { 1 } { \sqrt { 11 } + \sqrt { 10 } }$

Question 30

Multiply and simplify where possible. $$( - 13 \sqrt { 13 } ) ( - 121 \sqrt { 1,331 } )$$

A) $17,303 \sqrt { 11 }$
B) $1,573 \sqrt { 143 }$
C) $13 \sqrt { 143 }$
D) $17,303 \sqrt { 143 }$
E) $1,331 \sqrt { 143 }$

Question 31

Multiply and simplify where possible. $$\sqrt { 1,000 } \sqrt { 110 }$$

A) $11 \sqrt { 11 }$
B) $10 \sqrt { 11 }$
C) $100 \sqrt { 11 }$
D) $11 \sqrt { 10 }$
E) $1,000 \sqrt { 11 }$

Question 32

Use the product rule to simplify. $$3 \sqrt { 9 } \cdot \sqrt { 64 } \cdot \sqrt { 16 }$$

A)3
B)27648
C)288
D)8

Question 33

Find the value without using a calculator. $$\sqrt [ 3 ] { - 0.001 }$$

A)-0.1
B)0.1
C)0.3
D)-0.3
E)not a real number

Question 34

Write the quotient as the quotient of two radicals and simplify. $$\sqrt { \frac { 16 } { 25 } }$$

A) $\frac { 5 } { 4 }$
B) $\frac { 5 } { 6 }$
C) $\frac { 4 } { 5 }$
D) $\frac { 5 } { 5 }$
E) $\frac { 4 } { 6 }$

Question 35

Find the following product and express your answer in simplest radical form. $$( 4 \sqrt { 5 } - 5 \sqrt { 15 } ) ( 7 \sqrt { 27 } + \sqrt { 15 } )$$

A) $- 84 \sqrt { 15 } - 20 \sqrt { 3 } + 315 \sqrt { 5 } + 75$
B) $84 \sqrt { 15 } - 20 \sqrt { 5 } - 315 \sqrt { 3 } + 75$
C) $28 \sqrt { 3 } + 4 \sqrt { 5 } - 75$
D) $84 \sqrt { 15 } + 20 \sqrt { 3 } - 315 \sqrt { 5 } - 75 \sqrt { 27 }$
E) $84 \sqrt { 15 } + 20 \sqrt { 3 } - 315 \sqrt { 5 } - 75$

Question 36

Rationalize the denominator and simplify. The variable represents a positive real number. $$\frac { \sqrt { z } } { \sqrt { z } - 10 }$$

A) $\frac { 10 \sqrt { z } } { z - 100 }$
B) $\frac { z + 10 \sqrt { z } } { z - 10 }$
C) $\sqrt { Z }$
D) $\frac { 11 z } { z - 100 }$
E) $\frac { z + 10 \sqrt { z } } { z - 100 }$

Question 37

Simplify the radical. $$\sqrt { c ^ { 5 } }$$

A) $c ^ { 4 } \sqrt { c }$
B) $c ^ { 2 } \sqrt { c }$
C) $c ^ { 2 } \sqrt { c ^ { 2 } }$
D) $c ^ { 3 } \sqrt { c }$
E)none of the above

Question 38

Simplify the cube root. $$\sqrt [ 3 ] { - 320 a ^ { 3 } }$$

A) $- 4 a \sqrt [ 3 ] { 5 }$
B) $- 5 a \sqrt [ 3 ] { 5 }$
C) $- 4 a \sqrt [ 3 ] { 6 }$
D) $- 6 a ^ { 2 } \sqrt [ 3 ] { 5 }$
E) $- 12 a \sqrt [ 3 ] { 5 }$

Question 39

Simplify the expression. All variables represent positive numbers. $$\sqrt { \frac { 343 r ^ { 5 } s ^ { 8 } t } { 81 r ^ { 3 } s ^ { 4 } t } }$$

A) $\frac { 9 r s ^ { 2 } \sqrt { 7 } } { 7 }$
B) $\frac { 7 r ^ { 2 } s ^ { 2 } t \sqrt { 7 } } { 9 }$
C) $\frac { 49 r s ^ { 2 } \sqrt { 7 } } { 9 t }$
D) $\frac { 7 r s ^ { 2 } \sqrt { 7 } } { 9 }$
E) $\frac { 49 r s ^ { 2 } \sqrt { 7 } } { 9 }$

Question 40

Simplify the cube root. $$\sqrt [ 3 ] { 40 y ^ { 3 } }$$

A) $3 y ^ { 3 } \sqrt { 5 }$
B) $4 y ^ { 3 } \sqrt { 7 }$
C) $2 y ^ { 3 } \sqrt { 6 }$
D) $4 y ^ { 3 } \sqrt { 5 }$
E) $2 y ^ { 3 } \sqrt { 5 }$

Question 41

Simplify the cube root. $$\sqrt [ 3 ] { \frac { 189 p ^ { 6 } } { 1,000 p ^ { 2 } q ^ { 9 } } }$$

A) $\frac { 10 p \sqrt [ 3 ] { 7 } } { 3 q }$
B) $\frac { 3 p q \sqrt [ 3 ] { 7 } } { 10 }$
C) $\frac { 3 p \sqrt [ 3 ] { 7 } } { 10 q }$
D) $\frac { 3 q \sqrt [ 3 ] { 7 } } { 10 p }$
E) $\frac { 3 \sqrt [ 3 ] { 7 } } { 10 p q }$

Question 42

Use the distributive property to help simplify the expression. $$2 \sqrt [ 3 ] { 3 } + 4 \sqrt [ 3 ] { 81 } - 5 \sqrt [ 3 ] { 24 }$$

A) $6 \sqrt [ 3 ] { 3 }$
B) $- 4 \sqrt [ 3 ] { 3 }$
C) $- 4 \sqrt [ 3 ] { 2 }$
D) $4 \sqrt [ 3 ] { 3 }$
E) $4 \sqrt [ 3 ] { 2 }$

Question 43

Express the following expression in simplest radical form. All variables represent positive real numbers. $$\sqrt [ 3 ] { 16 x ^ { 9 } y ^ { 11 } }$$

A) $2 x ^ { 3 } y ^ { 6 } \sqrt [ 3 ] { 2 y ^ { 2 } }$
B) $2 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { 2 y ^ { 2 } }$
C) $2 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { 2 y }$
D) $2 x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { 2 y ^ { 2 } }$
E) $2 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { y }$

Question 44

Simplify the expression by using the distributive property. $$9 \sqrt { 3 } + 5 \sqrt { 3 }$$

A) $26$
B) $45 \sqrt { 3 }$
C) $14 \sqrt { 3 }$
D) $4 \sqrt { 3 }$
E) $13 \sqrt { 3 }$

Question 45

Do the multiplication. $( 7 \sqrt [ 3 ] { 3 } ) ( 2 \sqrt [ 3 ] { 5 } )$

A)14
B) $14 \sqrt [ 3 ] { 15 }$
C) $14 \sqrt [ 3 ] { 8 }$
D)28
E)none of the above

Question 46

Use the distributive property to help simplify the expression. $$10 \sqrt { 27 } - 2 \sqrt { 3 } - 4 \sqrt { 48 }$$

A) $4 \sqrt { 27 }$
B) $7 \sqrt { 3 }$
C) $12 \sqrt { 3 }$
D) $19 \sqrt { 3 }$
E) $10 \sqrt { 3 }$

Question 47

Do the multiplication. $$( \sqrt { 7 } - 7 ) ( \sqrt { 7 } + 7 )$$

A) $7 + \sqrt { 7 }$
B)56
C) $49 - 14 \sqrt { 7 } + 7$
D)-42
E) $7 + 2 \sqrt { 7 }$

Question 48

Simplify the following expression. $$4 \sqrt { 63 } + 4 \sqrt { 7 }$$

A) $8 \sqrt { 7 }$
B) $112$
C) $16 \sqrt [ 3 ] { 7 }$
D) $8 \sqrt [ 3 ] { 7 }$
E) $16 \sqrt { 7 }$

Question 49

Evaluate the expression. $$( 9 \sqrt { 5 } ) ^ { 2 }$$

A)403
B)405
C)225
D)385
E)415

Question 50

Perform the multiplication. The variable represents a positive number.

A)25 y
B)5 y ⁴
C)25 y ⁴
D)5 y
E)25 y ³

Question 51

Evaluate the expression.

Question 52

Use the distributive property to help simplify the expression. $$4 \sqrt { 125 } - 2 \sqrt { 5 }$$

A) $20 \sqrt { 5 }$
B) $18 \sqrt { 5 }$
C) $2 \sqrt { 5 }$
D) $2 \sqrt { 120 }$
E) $98 \sqrt { 5 }$

Question 53

Do the multiplication. $$( \sqrt [ 3 ] { 3 } - 9 ) ( \sqrt [ 3 ] { 3 } - 4 )$$

A) $\sqrt [ 3 ] { 9 } - 13 \sqrt [ 3 ] { 3 } - 36$
B) $\sqrt [ 3 ] { 9 } + 13 \sqrt [ 3 ] { 3 } + 36$
C) $\sqrt [ 3 ] { 9 } - 13 \sqrt [ 3 ] { 3 } + 36$
D) $\sqrt [ 3 ] { 9 } + 13 \sqrt [ 3 ] { 3 } - 36$
E)none of the above

Question 54

Evaluate the expression. $$( - \sqrt [ 2 ] { 14 } ) ^ { 2 }$$

A)196
B)24
C)-14
D)14
E)12

Question 55

Use the distributive property to help simplify the expression. $$\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }$$

A) $\frac { 12 } { 5 } \sqrt { 3 }$
B) $- \frac { 5 } { 12 } \sqrt { 3 }$
C) $- \frac { 5 } { 12 } \sqrt { 7 }$
D) $\frac { 5 } { 12 } \sqrt { 7 }$
E) $\frac { 5 } { 12 } \sqrt { 3 }$

Question 56

Express the following expression in simplest radical form. The variable represents a positive real number. $$\sqrt [ 3 ] { 24 y }$$

A) $4 \sqrt [ 3 ] { 3 y }$
B) $2 y ^ { 3 } \sqrt [ 3 ] { 3 }$
C) $2 \sqrt [ 3 ] { y }$
D) $\sqrt [ 3 ] { 3 y }$
E) $2 \sqrt [ 3 ] { 3 y }$

Question 57

Do the multiplication. All variables represent positive numbers. $$\sqrt { a } ( \sqrt { 3 a } - 3 )$$

A) $\sqrt { 3 } a + 4 \sqrt { a }$
B) $3 \sqrt { a } - a \sqrt { 4 }$
C) $\sqrt { 3 } a - 4 \sqrt { a }$
D) $\sqrt { 4 } a - 3 \sqrt { a }$
E)none of the above

Question 58

Express the following expression in simplest radical form. All variables represent positive real numbers. $$\frac { \sqrt [ 3 ] { 45 x y } } { \sqrt [ 3 ] { 5 x ^ { 2 } y ^ { 5 } } }$$

A) $\frac { 3 \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }$
B) $\frac { \sqrt [ 3 ] { 9 x y } } { y }$
C) $\frac { 9 \sqrt [ 3 ] { x y } } { x y ^ { 2 } }$
D) $\frac { \sqrt [ 3 ] { 9 x ^ { 2 } y ^ { 2 } } } { x y ^ { 2 } }$
E) $\frac { \sqrt [ 3 ] { 9 } } { x y ^ { 3 } }$

Question 59

Evaluate the expression. $$( \sqrt { 7 } ) ^ { 2 }$$

A)10
B)49
C)-7
D)7
E)8

Question 60

Simplify the expression. Assume that all variables represent positive numbers. $$\frac { \sqrt { 27 x y ^ { 2 } } } { \sqrt { 49 x } }$$

A) $\frac { 3 y \sqrt { 3 } } { 7 }$
B) $\frac { y \sqrt { 3 } } { 7 }$
C) $\frac { y \sqrt { 3 } } { 7 x }$
D) $\frac { 49 y \sqrt { 3 } } { 7 }$

Question 61

Solve the equation. Write all apparent solutions. Which of them are extraneous? $\sqrt { b } = 5$

A)5, 25
B)5, there are no extraneous solutions
C)25, there are no extraneous solutions
D)5 is extraneous, no solution
E)25 is extraneous, no solution

Question 62

Solve the equation. $\sqrt { x } - 25 = 0$

A)x = 75
B)x = 5
C)x = 25
D)x = 625
E)none of the above

Question 63

Solve the equation. $$\sqrt { 90 - 2 r } = \sqrt { 8 r + 10 }$$

A)r = 81
B)r = 8
C)r = 64
D)r = 9
E)no solution

Question 64

Solve the equation. Check all solutions. $$\sqrt { x - 6 } - 2 = 5$$

A)57
B)32
C)55
D)44
E)no solution

Question 65

Do the division by rationalizing the denominator and simplifying. Variables represent positive numbers. $$\frac { \sqrt { x } - 2 } { \sqrt { x } + 2 }$$

A) $\frac { x + 4 \sqrt { x } + 4 } { x - 4 }$
B) $\frac { x - 4 \sqrt { x } + 4 } { x + 4 }$
C) $\frac { x - 4 \sqrt { x } + 4 } { x - 4 }$
D) $\frac { x - 4 } { x + 4 \sqrt { x } + 4 }$
E)none of the above

Question 66

Solve the equation. Check all solutions. $$\sqrt { y } = 5$$

A)25
B)13
C)5
D)23
E)no solution

Question 67

Solve the equation. $$\sqrt { 5 c } = 10$$

A)4
B)3
C)2
D)5
E)20

Question 68

Solve the equation. $$\sqrt { 2 r + 69 } - 9 = 0$$

A) $r = \frac { 72 } { 2 }$
B)r = 36
C)r = 6
D)r = 20
E)no solution

Question 69

Do the division by rationalizing the denominator and simplifying. $$\frac { \sqrt [ 3 ] { 2 } } { \sqrt [ 3 ] { 3 } }$$

A) $\frac { \sqrt [ 3 ] { 18 } } { 9 }$
B) $\frac { \sqrt [ 3 ] { 6 } } { 3 }$
C) $\frac { \sqrt [ 3 ] { 18 } } { 3 }$
D) $\frac { \sqrt [ 3 ] { 18 } } { 9 }$ .
E) $\frac { \sqrt [ 3 ] { 18 } } { 3 }$ ..

Question 70

Solve the equation. $$\sqrt { 5 t - 2 } = \sqrt { t + 6 }$$

A)t = 3
B)t = 2
C)t = 1
D)t = 1, 3
E)no solution

Question 71

Solve the equation. $$x = \sqrt { x ^ { 2 } - 3 x + 15 }$$

A)x = 25
B)x = 5
C)x = ±25
D)x = -5
E)no solution

Question 72

Simplify the expression. Assume that all variables represent positive numbers. $$\frac { \sqrt [ 3 ] { 270 a ^ { 11 } } } { \sqrt [ 3 ] { 10 a ^ { 8 } } }$$

A) $9 a ^ { 2 }$
B) $3 a ^ { 2 }$
C) $5 a$
D) $9 a$
E) $3 a$

Question 73

Solve the equation. $$b - 10 = \sqrt { b ^ { 2 } - 380 }$$

A) $\frac { 1 - \sqrt { 1,481 } } { 2 }$
B) $\frac { 1 + \sqrt { 1,481 } } { 2 }$
C)24
D)34
E)no solution

Question 74

Solve the equation. $$2 \sqrt { 3 x + 7 } = \sqrt { 5 x + 14 }$$

A)0
B)2
C)-2
D)-2, 2
E)no solution

Question 75

Solve the equation. $$\sqrt { x + 10 } = 4$$

A)x = 16
B)x = -6
C)x = ±16
D)x = 6
E)no solution

Question 76

Solve the equation. Write all apparent solutions. Which of them are extraneous? $\sqrt { z } + 8 = 1$

A)7, 49
B)7, there are no extraneous solutions
C)49, there are no extraneous solutions
D)7 is extraneous, no solution
E)49 is extraneous, no solution

Question 77

Solve the equation. $$\sqrt { 4 m ^ { 2 } + 2 m + 6 } = - 2 m$$

A)m = 6
B)m = ±3
C)m = -3
D)m = -6
E)no solution

Question 78

Simplify the expression. Assume that all variables represent positive numbers. $$\frac { \sqrt { 100 x y ^ { 3 } } } { \sqrt { 25 x ^ { 3 } y } }$$

A) $\frac { 2 \sqrt { y } } { x ^ { 2 } }$
B) $\frac { 2 } { x }$
C) $\frac { 2 y } { x }$
D) $\frac { 2 y ^ { 2 } } { x }$
E) $\frac { 5 y } { \sqrt { x } }$

Question 79

Perform the division by rationalizing the denominator and simplifying. The variable represents a positive number. $$\frac { 8 } { \sqrt { x } }$$

A) $\frac { \sqrt { x } } { 8 }$
B) $\frac { 8 \sqrt { x } } { x }$
C) $8 \times \sqrt { x }$
D) $\frac { 8 \sqrt { x } } { x ^ { 2 } }$
E) 8
$x$

Question 80

Solve the equation. Write all apparent solutions. Which of them are extraneous? $$3 = 4 + \sqrt { 4 x + 67 }$$

A) $- \frac { 33 } { 2 }$ is extraneous solution, no solution
B) $- \frac { 35 } { 2 }$ is extraneous solution, $- \frac { 33 } { 2 }$
C) $- \frac { 35 } { 2 }$ is extraneous solution, no solution
D) $- \frac { 33 } { 2 }$
E) $- \frac { 35 } { 2 }$