Question 1

Simplify the radical expression. $\sqrt { 192 x ^ { 14 } y ^ { 13 } }$

Accepted Answer

A)  $8 x ^ { 6 } \left| y ^ { 7 } \right| \sqrt { 3 x }$ 
B)  $24 x ^ { 6 } \left| y ^ { 7 } \right| \sqrt { x }$ 
C)  $8 \left| x ^ { 7 } \right| y ^ { 6 } \sqrt { 3 y }$ 
D)  $24 \left| x ^ { 7 } \right| y ^ { 6 } \sqrt { y }$ 
E)  $8 \left| x ^ { 8 } \right| y ^ { 7 } \sqrt { 3 y }$ 
A)  $8 x ^ { 6 } \left| y ^ { 7 } \right| \sqrt { 3 x }$ 
B)  $24 x ^ { 6 } \left| y ^ { 7 } \right| \sqrt { x }$ 
C)  $8 \left| x ^ { 7 } \right| y ^ { 6 } \sqrt { 3 y }$ 
D)  $24 \left| x ^ { 7 } \right| y ^ { 6 } \sqrt { y }$ 
E)  $8 \left| x ^ { 8 } \right| y ^ { 7 } \sqrt { 3 y }$

Question 2

Simplify the expression $\sqrt { 64 x } + \sqrt { 9 x }$ .

Accepted Answer

A)  $\sqrt { x }$ 
B)  67 $\sqrt { x }$ 
C)  11x 
D)  11 $\sqrt { x }$ 
E)  $\sqrt { 11 }$ x 
A)  $\sqrt { x }$ 
B)  67 $\sqrt { x }$ 
C)  11x 
D)  11 $\sqrt { x }$ 
E)  $\sqrt { 11 }$ x

Question 3

Determine which value of x is a solution of $\sqrt { x } - 8 = 0$ .

Accepted Answer

A)  x=128 
B)  x=8 
C)  x=0 
D)  x=-8 
E)  x=64 
A)  x=128 
B)  x=8 
C)  x=0 
D)  x=-8 
E)  x=64

Question 4

Rewrite the expression using rational exponents. $\sqrt [ 4 ] { y ^ { 3 } } \sqrt [ 3 ] { y }$

Accepted Answer

A)  $y ^ { \frac { 1 } { 6 } }$ 
B)  $y ^ { \frac { 13 } { 12 } }$ 
C)  $y ^ { \frac { 1 } { 4 } }$ 
D)  $y ^ { \frac { 1 } { 3 } }$ 
E)  $y ^ { \frac { 3 } { 4 } }$ 
A)  $y ^ { \frac { 1 } { 6 } }$ 
B)  $y ^ { \frac { 13 } { 12 } }$ 
C)  $y ^ { \frac { 1 } { 4 } }$ 
D)  $y ^ { \frac { 1 } { 3 } }$ 
E)  $y ^ { \frac { 3 } { 4 } }$

Question 5

Rationalize the denominator and simplify the expression $\sqrt [ 3 ] { \frac { 1 } { 512 y ^ { 2 } } }$ .

Accepted Answer

A)  $\frac { 1 } { 8 y }$ 
B)  $\frac { \sqrt [ 3 ] { y } } { 8 }$ 
C)  $\frac { \sqrt [ 3 ] { y } } { 8 y }$ 
D)  $\frac { \sqrt [ 3 ] { y } } { y }$ 
E)  $\frac { \sqrt { y } } { 8 y }$ 
A)  $\frac { 1 } { 8 y }$ 
B)  $\frac { \sqrt [ 3 ] { y } } { 8 }$ 
C)  $\frac { \sqrt [ 3 ] { y } } { 8 y }$ 
D)  $\frac { \sqrt [ 3 ] { y } } { y }$ 
E)  $\frac { \sqrt { y } } { 8 y }$

Question 6

Rationalize the denominator and simplify the expression $\frac { 2 } { \sqrt { z } }$ .

Accepted Answer

A)  $\frac { 2 \sqrt { z } } { z ^ { 2 } }$ 
B)  $\frac { 2 \sqrt { z } } { z }$ 
C)  2 
D)  $2 \sqrt { z }$ 
E)  $\frac { 2 + \sqrt { z } } { z }$ 
A)  $\frac { 2 \sqrt { z } } { z ^ { 2 } }$ 
B)  $\frac { 2 \sqrt { z } } { z }$ 
C)  2 
D)  $2 \sqrt { z }$ 
E)  $\frac { 2 + \sqrt { z } } { z }$

Question 7

Combine the radical expression, if possible. $\sqrt { 36 x - 72 } + \sqrt { x - 2 }$

Accepted Answer

A)  $6 \sqrt { 2 ( x - 2 ) }$ 
B)  $8 \sqrt { x - 2 }$ 
C)  $7 \sqrt { x - 2 }$ 
D)  $7 \sqrt { 2 ( x - 2 ) }$ 
E)  $6 \sqrt { x - 2 }$ 
A)  $6 \sqrt { 2 ( x - 2 ) }$ 
B)  $8 \sqrt { x - 2 }$ 
C)  $7 \sqrt { x - 2 }$ 
D)  $7 \sqrt { 2 ( x - 2 ) }$ 
E)  $6 \sqrt { x - 2 }$

Question 8

Simplify the expression $\frac { 13 y ^ { 4 / 3 } z ^ { - 1 / 5 } } { 28 y ^ { - 2 / 3 } z }$ .

Accepted Answer

A)  $\frac { 14 y ^ { 2 } } { 29 z ^ { 6 / 5 } }$ 
B)  $\frac { 13 y ^ { 2 } } { 28 z ^ { 6 / 5 } }$ 
C)  $\frac { 13 y ^ { 2 } } { 28 z ^ { 4 / 5 } }$ 
D)  $\frac { 13 y ^ { 2 } } { 28 z ^ { 1 / 5 } }$ 
E)  $\frac { y ^ { 2 } } { 2 z ^ { 6 / 5 } }$ 
A)  $\frac { 14 y ^ { 2 } } { 29 z ^ { 6 / 5 } }$ 
B)  $\frac { 13 y ^ { 2 } } { 28 z ^ { 6 / 5 } }$ 
C)  $\frac { 13 y ^ { 2 } } { 28 z ^ { 4 / 5 } }$ 
D)  $\frac { 13 y ^ { 2 } } { 28 z ^ { 1 / 5 } }$ 
E)  $\frac { y ^ { 2 } } { 2 z ^ { 6 / 5 } }$

Question 9

Simplify the radical expression. $\sqrt [ 4 ] { 64 u ^ { 4 } v ^ { 7 } }$

Accepted Answer

A)  $8 | u | v \sqrt [ 4 ] { v ^ { 4 } }$ 
B)  $4 | u | v ^ { 3 } \sqrt [ 4 ] { 2 }$ 
C)  $8 | u | v ^ { 6 } \sqrt [ 4 ] { v }$ 
D)  $4 | u | v ^ { 2 } \sqrt [ 4 ] { 2 v }$ 
E)  $2 | u | v \sqrt [ 4 ] { 4 v ^ { 3 } }$ 
A)  $8 | u | v \sqrt [ 4 ] { v ^ { 4 } }$ 
B)  $4 | u | v ^ { 3 } \sqrt [ 4 ] { 2 }$ 
C)  $8 | u | v ^ { 6 } \sqrt [ 4 ] { v }$ 
D)  $4 | u | v ^ { 2 } \sqrt [ 4 ] { 2 v }$ 
E)  $2 | u | v \sqrt [ 4 ] { 4 v ^ { 3 } }$

Question 10

Write $\frac { 13 } { 2 + 2 i }$ in standard form.

Accepted Answer

A)  $\frac { 13 } { 2 } + \frac { 13 } { 2 } i$ 
B)  $- \frac { 13 } { 4 } + \frac { 13 } { 4 } i$ 
C)  $\frac { 13 } { 4 } + \frac { 13 } { 4 } i$ 
D)  $\frac { 13 } { 4 } + 26 i$ 
E)  $\frac { 13 } { 4 } - \frac { 13 } { 4 } i$ 
A)  $\frac { 13 } { 2 } + \frac { 13 } { 2 } i$ 
B)  $- \frac { 13 } { 4 } + \frac { 13 } { 4 } i$ 
C)  $\frac { 13 } { 4 } + \frac { 13 } { 4 } i$ 
D)  $\frac { 13 } { 4 } + 26 i$ 
E)  $\frac { 13 } { 4 } - \frac { 13 } { 4 } i$

Question 11

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 3 ] { ( - 9 ) ^ { 3 } }$

Accepted Answer

A)  729 
B)  -729 
C)  -9 
D)  9 
E) not possible 
A)  729 
B)  -729 
C)  -9 
D)  9 
E) not possible

Question 12

Multiply the expression by its conjugate and simplify. $\sqrt { 14 } - 10$

Accepted Answer

A)  -86 
B)  186 
C)  96 
D) 1 
E) 0 
A)  -86 
B)  186 
C)  96 
D) 1 
E) 0

Question 13

The time t , in seconds, for a pendulum of length L , in feet, to go through one complete cycle both forward and backward (its period), is given by $t = 2 \pi \sqrt { \frac { L } { 32 } }$ . How long is a pendulum of a grandfather clock with a period of 1.4 seconds? Round your answer to two decimal places.

Accepted Answer

A)  4.99 feet 
B)  1.59 feet 
C)  2.5 feet 
D)  1.13 feet 
E)  3.18 feet 
A)  4.99 feet 
B)  1.59 feet 
C)  2.5 feet 
D)  1.13 feet 
E)  3.18 feet

Question 14

Is $9 - 6 i$ a solution of the equation $$x ^ { 2 } - 18 x + 117 = 0 ?$$

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 15

Evaluate without using a calculator. $\left( - 2 ^ { 3 } \right) ^ { \frac { 5 } { 3 } }$

Accepted Answer

A) -32 
B) -8 
C) 8 
D) 5 
E) 32 
A) -32 
B) -8 
C) 8 
D) 5 
E) 32

Question 16

Write the number in i -form. $\frac { \sqrt { - 441 } } { \sqrt { - 9 } }$

Accepted Answer

A) 9 
B) 7 
C)  $- 9 i$ 
D) 7i 
E)  $7 + 9 i$ 
A) 9 
B) 7 
C)  $- 9 i$ 
D) 7i 
E)  $7 + 9 i$

Question 17

Rewrite the expression using rational exponents. $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 / 3 } }$ 
B)  $x ^ { 3 }$ 
C)  $\frac { 1 } { x ^ { 2 } }$ 
D)  $\frac { 1 } { x ^ { 3 } }$ 
E)  $x ^ { 2 }$ 
A)  $\frac { 1 } { x ^ { 2 / 3 } }$ 
B)  $x ^ { 3 }$ 
C)  $\frac { 1 } { x ^ { 2 } }$ 
D)  $\frac { 1 } { x ^ { 3 } }$ 
E)  $x ^ { 2 }$

Question 18

Simplify the radical $\sqrt { \frac { 5 x ^ { 4 } } { 45 } }$ .

Accepted Answer

A)  $x ^ { 2 }$ 
B)  $\frac { x ^ { 2 } } { 3 }$ 
C)  $\frac { x } { 3 }$ 
D)  $\frac { 1 } { 3 }$ 
E)  $x ^ { 2 } \sqrt { 5 }$ 
A)  $x ^ { 2 }$ 
B)  $\frac { x ^ { 2 } } { 3 }$ 
C)  $\frac { x } { 3 }$ 
D)  $\frac { 1 } { 3 }$ 
E)  $x ^ { 2 } \sqrt { 5 }$

Question 19

Determine the values of a and b that satisfy the equation. $$8 - 7 i = ( a + 4 ) + ( b - 9 ) i$$

Accepted Answer

A)  $a = 4 ; b = 2$ 
B)  $a = 12 ; b = 16$ 
C)  $a = 17 ; b = 11$ 
D)  $a = 1 ; b = - 5$ 
E)  $a = - 2 ; b = - 4$ 
A)  $a = 4 ; b = 2$ 
B)  $a = 12 ; b = 16$ 
C)  $a = 17 ; b = 11$ 
D)  $a = 1 ; b = - 5$ 
E)  $a = - 2 ; b = - 4$

Question 20

Solve the equation. $4 y ^ { \frac { 1 } { 3 } } = 5$

Accepted Answer

A)  $y = \frac { 125 } { 64 }$ 
B)  $y = \frac { 5 } { 4 }$ 
C)  $y = \frac { 125 } { 64 }$ 
D)  $y = - \frac { 5 } { 4 }$ 
E) no solution 
A)  $y = \frac { 125 } { 64 }$ 
B)  $y = \frac { 5 } { 4 }$ 
C)  $y = \frac { 125 } { 64 }$ 
D)  $y = - \frac { 5 } { 4 }$ 
E) no solution

Simplify the radical expression. $\sqrt { 192 x ^ { 14 } y ^ { 13 } }$

Simplify the expression $\sqrt { 64 x } + \sqrt { 9 x }$ .

Determine which value of x is a solution of $\sqrt { x } - 8 = 0$ .

Rewrite the expression using rational exponents. $\sqrt [ 4 ] { y ^ { 3 } } \sqrt [ 3 ] { y }$

Rationalize the denominator and simplify the expression $\sqrt [ 3 ] { \frac { 1 } { 512 y ^ { 2 } } }$ .

Rationalize the denominator and simplify the expression $\frac { 2 } { \sqrt { z } }$ .

Combine the radical expression, if possible. $\sqrt { 36 x - 72 } + \sqrt { x - 2 }$

Simplify the expression $\frac { 13 y ^ { 4 / 3 } z ^ { - 1 / 5 } } { 28 y ^ { - 2 / 3 } z }$ .

Simplify the radical expression. $\sqrt [ 4 ] { 64 u ^ { 4 } v ^ { 7 } }$

Write $\frac { 13 } { 2 + 2 i }$ in standard form.

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 3 ] { ( - 9 ) ^ { 3 } }$

Multiply the expression by its conjugate and simplify. $\sqrt { 14 } - 10$

Is $9 - 6 i$ a solution of the equation $x ^ { 2 } - 18 x + 117 = 0 ?$

Evaluate without using a calculator. $\left( - 2 ^ { 3 } \right) ^ { \frac { 5 } { 3 } }$

Write the number in i -form. $\frac { \sqrt { - 441 } } { \sqrt { - 9 } }$

Rewrite the expression using rational exponents. $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$

Simplify the radical $\sqrt { \frac { 5 x ^ { 4 } } { 45 } }$ .

Determine the values of a and b that satisfy the equation. $8 - 7 i = ( a + 4 ) + ( b - 9 ) i$

Solve the equation. $4 y ^ { \frac { 1 } { 3 } } = 5$

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Radicals and Complex Numbers

Simplify the radical expression. 192x14y13\sqrt { 192 x ^ { 14 } y ^ { 13 } }192x14y13​

Simplify the expression 64x+9x\sqrt { 64 x } + \sqrt { 9 x }64x​+9x​ .

Determine which value of x is a solution of x−8=0\sqrt { x } - 8 = 0x​−8=0 .

Rewrite the expression using rational exponents. y34y3\sqrt [ 4 ] { y ^ { 3 } } \sqrt [ 3 ] { y }4y3​3y​

Rationalize the denominator and simplify the expression 1512y23\sqrt [ 3 ] { \frac { 1 } { 512 y ^ { 2 } } }3512y21​​ .

Rationalize the denominator and simplify the expression 2z\frac { 2 } { \sqrt { z } }z​2​ .

Combine the radical expression, if possible. 36x−72+x−2\sqrt { 36 x - 72 } + \sqrt { x - 2 }36x−72​+x−2​

Simplify the expression 13y4/3z−1/528y−2/3z\frac { 13 y ^ { 4 / 3 } z ^ { - 1 / 5 } } { 28 y ^ { - 2 / 3 } z }28y−2/3z13y4/3z−1/5​ .

Simplify the radical expression. 64u4v74\sqrt [ 4 ] { 64 u ^ { 4 } v ^ { 7 } }464u4v7​

Write 132+2i\frac { 13 } { 2 + 2 i }2+2i13​ in standard form.

Evaluate the radical expression (if possible)without using a calculator. −(−9)33- \sqrt [ 3 ] { ( - 9 ) ^ { 3 } }−3(−9)3​

Multiply the expression by its conjugate and simplify. 14−10\sqrt { 14 } - 1014​−10

Is 9−6i9 - 6 i9−6i a solution of the equation x2−18x+117=0?x ^ { 2 } - 18 x + 117 = 0 ?x2−18x+117=0?

Evaluate without using a calculator. (−23)53\left( - 2 ^ { 3 } \right) ^ { \frac { 5 } { 3 } }(−23)35​

Write the number in i -form. −441−9\frac { \sqrt { - 441 } } { \sqrt { - 9 } }−9​−441​​

Rewrite the expression using rational exponents. x53x73\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }3x7​3x5​​

Simplify the radical 5x445\sqrt { \frac { 5 x ^ { 4 } } { 45 } }455x4​​ .

Determine the values of a and b that satisfy the equation. 8−7i=(a+4)+(b−9)i8 - 7 i = ( a + 4 ) + ( b - 9 ) i8−7i=(a+4)+(b−9)i

Solve the equation. 4y13=54 y ^ { \frac { 1 } { 3 } } = 54y31​=5

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Simplify the radical expression. $\sqrt { 192 x ^ { 14 } y ^ { 13 } }$

Simplify the expression $\sqrt { 64 x } + \sqrt { 9 x }$ .

Determine which value of x is a solution of $\sqrt { x } - 8 = 0$ .

Rewrite the expression using rational exponents. $\sqrt [ 4 ] { y ^ { 3 } } \sqrt [ 3 ] { y }$

Rationalize the denominator and simplify the expression $\sqrt [ 3 ] { \frac { 1 } { 512 y ^ { 2 } } }$ .

Rationalize the denominator and simplify the expression $\frac { 2 } { \sqrt { z } }$ .

Combine the radical expression, if possible. $\sqrt { 36 x - 72 } + \sqrt { x - 2 }$

Simplify the expression $\frac { 13 y ^ { 4 / 3 } z ^ { - 1 / 5 } } { 28 y ^ { - 2 / 3 } z }$ .

Simplify the radical expression. $\sqrt [ 4 ] { 64 u ^ { 4 } v ^ { 7 } }$

Write $\frac { 13 } { 2 + 2 i }$ in standard form.

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 3 ] { ( - 9 ) ^ { 3 } }$

Multiply the expression by its conjugate and simplify. $\sqrt { 14 } - 10$

Is $9 - 6 i$ a solution of the equation $x ^ { 2 } - 18 x + 117 = 0 ?$

Evaluate without using a calculator. $\left( - 2 ^ { 3 } \right) ^ { \frac { 5 } { 3 } }$

Write the number in i -form. $\frac { \sqrt { - 441 } } { \sqrt { - 9 } }$

Rewrite the expression using rational exponents. $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$

Simplify the radical $\sqrt { \frac { 5 x ^ { 4 } } { 45 } }$ .

Determine the values of a and b that satisfy the equation. $8 - 7 i = ( a + 4 ) + ( b - 9 ) i$

Solve the equation. $4 y ^ { \frac { 1 } { 3 } } = 5$