Question 1

Use the Pythagorean theorem to find the unknown side of the right triangle.
-

Accepted Answer

A)  128 
B)  8 
C)  16 
D)  256 
A)  128 
B)  8 
C)  16 
D)  256

Question 2

Find all real square roots of the number.
$\frac { 4 } { 121 }$

Accepted Answer

A)  $\frac { 1 } { 30 } , - \frac { 1 } { 30 }$ 
B)  $\frac { 1 } { 6 } , - \frac { 1 } { 6 }$ 
C)  $\frac { 3 } { 11 } , - \frac { 3 } { 11 }$ 
D)  $\frac { 2 } { 11 } , - \frac { 2 } { 11 }$ 
A)  $\frac { 1 } { 30 } , - \frac { 1 } { 30 }$ 
B)  $\frac { 1 } { 6 } , - \frac { 1 } { 6 }$ 
C)  $\frac { 3 } { 11 } , - \frac { 3 } { 11 }$ 
D)  $\frac { 2 } { 11 } , - \frac { 2 } { 11 }$

Question 3

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
-$\sqrt { 618 }$

Accepted Answer

A)  $618.000$ 
B)  $24.857$ 
C)  $24.865$ 
D)  $24.860$ 
A)  $618.000$ 
B)  $24.857$ 
C)  $24.865$ 
D)  $24.860$

Question 4

Write with positive exponents. Simplify if possible.
-$( - 64 ) ^ { - 2 / 3 }$

Accepted Answer

A)  $- 16$ 
B)  $\frac { 1 } { 16 }$ 
C) $ - \frac { 1 } { 16 }$ 
D)  $\frac { 128 } { 3 }$ 
A)  $- 16$ 
B)  $\frac { 1 } { 16 }$ 
C) $ - \frac { 1 } { 16 }$ 
D)  $\frac { 128 } { 3 }$

Question 5

Find the cube root.
-$$\sqrt [ 3 ] { - 125 x ^ { 36 } y ^ { 12 } }$$

Accepted Answer

A)  $5 x ^ { 12 } y ^ { 4 }$ 
B)  $25 \mathrm { x } ^ { 12 } \mathrm { y } ^ { 4 }$ 
C)  $- 5 x ^ { 18 } y ^ { 6 }$ 
D)  $- 5 x ^ { 12 } y ^ { 4 }$ 
A)  $5 x ^ { 12 } y ^ { 4 }$ 
B)  $25 \mathrm { x } ^ { 12 } \mathrm { y } ^ { 4 }$ 
C)  $- 5 x ^ { 18 } y ^ { 6 }$ 
D)  $- 5 x ^ { 12 } y ^ { 4 }$

Question 6

Provide an appropriate response.
-Find the distance between the points $( - 3 , - 6 )$ and $( 7 , - 1 )$.

Accepted Answer

A)  $75 \sqrt { 3 }$ units 
B)  75 units 
C)  5 units 
D)  $5 \sqrt { 5 }$ units 
A)  $75 \sqrt { 3 }$ units 
B)  75 units 
C)  5 units 
D)  $5 \sqrt { 5 }$ units

Question 7

Use the Pythagorean theorem to find the unknown side of the right triangle.
-

Accepted Answer

A)  18 
B)  24 
C)  25 
D)  20 
A)  18 
B)  24 
C)  25 
D)  20

Question 8

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )$

Accepted Answer

A)  $10 \sqrt { 5 }$ 
B)  $\sqrt { 15 } + \sqrt { 35 }$ 
C)  $5 \sqrt { 3 } + 5 \sqrt { 7 }$ 
D)  $\sqrt { 50 }$ 
A)  $10 \sqrt { 5 }$ 
B)  $\sqrt { 15 } + \sqrt { 35 }$ 
C)  $5 \sqrt { 3 } + 5 \sqrt { 7 }$ 
D)  $\sqrt { 50 }$

Question 9

Perform the indicated operation. Write the result in the form a + bi.
-$( 18 - 6 i ) ( 3 + i )$

Accepted Answer

A)  48 
B)  $60 - 36 i$ 
C)  $60 - 18 \mathrm { i }$ 
D)  60 
A)  48 
B)  $60 - 36 i$ 
C)  $60 - 18 \mathrm { i }$ 
D)  60

Question 10

Perform the indicated operation and simplify. Write the result in the form a + bi.
-$- \sqrt { - 292 }$

Accepted Answer

A)  $2 \sqrt { 73 }$ 
B)  $- 2 \sqrt { 73 }$ 
C)  $2 i \sqrt { 73 }$ 
D)  $- 2 i \sqrt { 73 }$ 
A)  $2 \sqrt { 73 }$ 
B)  $- 2 \sqrt { 73 }$ 
C)  $2 i \sqrt { 73 }$ 
D)  $- 2 i \sqrt { 73 }$

Question 11

Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 3 } { 2 + 7 i }$

Accepted Answer

A)  $\frac { 6 } { 53 } - \frac { 21 } { 53 } \mathrm { i }$ 
B)  $- \frac { 2 } { 15 } + \frac { 7 } { 15 } \mathrm { i }$ 
C)  $- \frac { 2 } { 15 } - \frac { 7 } { 15 } \mathrm { i }$ 
D)  $\frac { 6 } { 53 } + \frac { 21 } { 53 } \mathrm { i }$ 
A)  $\frac { 6 } { 53 } - \frac { 21 } { 53 } \mathrm { i }$ 
B)  $- \frac { 2 } { 15 } + \frac { 7 } { 15 } \mathrm { i }$ 
C)  $- \frac { 2 } { 15 } - \frac { 7 } { 15 } \mathrm { i }$ 
D)  $\frac { 6 } { 53 } + \frac { 21 } { 53 } \mathrm { i }$

Question 12

Use radical notation to write the expression. Simplify if possible.
-$$- 36^{1 / 2}$$

Accepted Answer

A)  12 
B)  - 18 
C)  -6 
D)  24 
A)  12 
B)  - 18 
C)  -6 
D)  24

Question 13

Provide an appropriate response.
-Find the midpoint of the line segment whose endpoints are $( - 6,4 )$ and $( - 18,14 )$.

Accepted Answer

A)  $( - 24,18 )$ 
B)  $( - 12,9 )$ 
C)  $( 12 , - 5 )$ 
D)  $( - 24 , - 9 )$ 
A)  $( - 24,18 )$ 
B)  $( - 12,9 )$ 
C)  $( 12 , - 5 )$ 
D)  $( - 24 , - 9 )$

Question 14

Solve.
-$\sqrt { x } - 3 = \sqrt { x - 27 }$

Accepted Answer

A)  $x = - 36$ 
B)  $x = 6$ 
C)  $x = 36$ 
D)  $\varnothing$ 
A)  $x = - 36$ 
B)  $x = 6$ 
C)  $x = 36$ 
D)  $\varnothing$

Question 15

Find the midpoint of the line segment whose endpoints are given.
-$$( - 9 \sqrt { 6 } , 8 \sqrt { 6 } ) , ( - 4 \sqrt { 6 } , 11 \sqrt { 6 } )$$

Accepted Answer

A)  $\left( \frac { - 5 \sqrt { 6 } } { 2 } , \frac { - 3 \sqrt { 6 } } { 2 } \right)$ 
B)  $\left( \frac { - 13 \sqrt { 6 } } { 2 } , \frac { 19 \sqrt { 6 } } { 2 } \right)$ 
C)  $( - 13 \sqrt { 6 } , 19 \sqrt { 6 } )$ 
D)  $\left( \frac { 5 \sqrt { 6 } } { 2 } , \frac { 3 \sqrt { 6 } } { 2 } \right)$ 
A)  $\left( \frac { - 5 \sqrt { 6 } } { 2 } , \frac { - 3 \sqrt { 6 } } { 2 } \right)$ 
B)  $\left( \frac { - 13 \sqrt { 6 } } { 2 } , \frac { 19 \sqrt { 6 } } { 2 } \right)$ 
C)  $( - 13 \sqrt { 6 } , 19 \sqrt { 6 } )$ 
D)  $\left( \frac { 5 \sqrt { 6 } } { 2 } , \frac { 3 \sqrt { 6 } } { 2 } \right)$

Question 16

Perform the indicated operation. Write the result in the form a + bi.
-$$( 7 + 3 i ) + ( 2 - 3 i )$$

Accepted Answer

A)  $9 + 6 i$ 
B)  9 
C)  $- 9$ 
D)  $9 + i$ 
A)  $9 + 6 i$ 
B)  9 
C)  $- 9$ 
D)  $9 + i$

Question 17

Use radical notation to write the expression. Simplify if possible.
-$$( 2 x + 2 ) ^ { 2 / 3 }$$

Accepted Answer

A)  $\sqrt [ 3 ] { 4 x ^ { 2 } + 4 }$ 
B)  $\sqrt [ 2 ] { ( 2 x + 2 ) ^ { 3 } }$ 
C)  $\sqrt [ 3 ] { ( 2 x + 2 ) ^ { 2 } }$ 
D)  $\sqrt [ 3 ] { 2 x ^ { 2 } + 4 }$ 
A)  $\sqrt [ 3 ] { 4 x ^ { 2 } + 4 }$ 
B)  $\sqrt [ 2 ] { ( 2 x + 2 ) ^ { 3 } }$ 
C)  $\sqrt [ 3 ] { ( 2 x + 2 ) ^ { 2 } }$ 
D)  $\sqrt [ 3 ] { 2 x ^ { 2 } + 4 }$

Question 18

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$$( 7 + \sqrt [ 3 ] { 2 } ) ( 7 - \sqrt [ 3 ] { 2 } )$$

Accepted Answer

A)  $49 - \sqrt [ 3 ] { 4 }$ 
B)  47 
C)  45 
D)  $49 - \sqrt [ 3 ] { 2 }$ 
A)  $49 - \sqrt [ 3 ] { 4 }$ 
B)  47 
C)  45 
D)  $49 - \sqrt [ 3 ] { 2 }$

Question 19

Find the distance between the pair of points.
-$( - 2 , - 2 )$ and $( 4,2 )$

Accepted Answer

A)  2 units 
B)  20 units 
C)  $20 \sqrt { 5 }$ units 
D)  $2 \sqrt { 13 }$ units 
A)  2 units 
B)  20 units 
C)  $20 \sqrt { 5 }$ units 
D)  $2 \sqrt { 13 }$ units

Question 20

Solve.
-$$\sqrt { 5 x + 4 } = \sqrt { 3 x + 1 } + 3$$

Accepted Answer

A)  0,5 
B)  33 
C)  0,33 
D)  $\varnothing$ 
A)  0,5 
B)  33 
C)  0,33 
D)  $\varnothing$

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Find all real square roots of the number. $\frac { 4 } { 121 }$

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - $\sqrt { 618 }$

Write with positive exponents. Simplify if possible. - $( - 64 ) ^ { - 2 / 3 }$

Find the cube root. - $\sqrt [ 3 ] { - 125 x ^ { 36 } y ^ { 12 } }$

Provide an appropriate response. -Find the distance between the points $( - 3 , - 6 )$ and $( 7 , - 1 )$ .

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )$

Perform the indicated operation. Write the result in the form a + bi. - $( 18 - 6 i ) ( 3 + i )$

Perform the indicated operation and simplify. Write the result in the form a + bi. - $- \sqrt { - 292 }$

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 3 } { 2 + 7 i }$

Use radical notation to write the expression. Simplify if possible. - $- 36^{1 / 2}$

Provide an appropriate response. -Find the midpoint of the line segment whose endpoints are $( - 6,4 )$ and $( - 18,14 )$ .

Solve. - $\sqrt { x } - 3 = \sqrt { x - 27 }$

Find the midpoint of the line segment whose endpoints are given. - $( - 9 \sqrt { 6 } , 8 \sqrt { 6 } ) , ( - 4 \sqrt { 6 } , 11 \sqrt { 6 } )$

Perform the indicated operation. Write the result in the form a + bi. - $( 7 + 3 i ) + ( 2 - 3 i )$

Use radical notation to write the expression. Simplify if possible. - $( 2 x + 2 ) ^ { 2 / 3 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( 7 + \sqrt [ 3 ] { 2 } ) ( 7 - \sqrt [ 3 ] { 2 } )$

Find the distance between the pair of points. - $( - 2 , - 2 )$ and $( 4,2 )$

Solve. - $\sqrt { 5 x + 4 } = \sqrt { 3 x + 1 } + 3$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 7: Rational Exponents, Radicals, and Complex Numbers

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Find all real square roots of the number. 4121\frac { 4 } { 121 }1214​

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - 618\sqrt { 618 }618​

Write with positive exponents. Simplify if possible. - (−64)−2/3( - 64 ) ^ { - 2 / 3 }(−64)−2/3

Find the cube root. - −125x36y123\sqrt [ 3 ] { - 125 x ^ { 36 } y ^ { 12 } }3−125x36y12​

Provide an appropriate response. -Find the distance between the points (−3,−6)( - 3 , - 6 )(−3,−6) and (7,−1)( 7 , - 1 )(7,−1) .

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - 5(3+7)\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )5​(3​+7​)

Perform the indicated operation. Write the result in the form a + bi. - (18−6i)(3+i)( 18 - 6 i ) ( 3 + i )(18−6i)(3+i)

Perform the indicated operation and simplify. Write the result in the form a + bi. - −−292- \sqrt { - 292 }−−292​

Perform the indicated operation. Write the result in the form a + bi. - 32+7i\frac { 3 } { 2 + 7 i }2+7i3​

Use radical notation to write the expression. Simplify if possible. - −361/2- 36^{1 / 2}−361/2

Provide an appropriate response. -Find the midpoint of the line segment whose endpoints are (−6,4)( - 6,4 )(−6,4) and (−18,14)( - 18,14 )(−18,14) .

Solve. - x−3=x−27\sqrt { x } - 3 = \sqrt { x - 27 }x​−3=x−27​

Find the midpoint of the line segment whose endpoints are given. - (−96,86),(−46,116)( - 9 \sqrt { 6 } , 8 \sqrt { 6 } ) , ( - 4 \sqrt { 6 } , 11 \sqrt { 6 } )(−96​,86​),(−46​,116​)

Perform the indicated operation. Write the result in the form a + bi. - (7+3i)+(2−3i)( 7 + 3 i ) + ( 2 - 3 i )(7+3i)+(2−3i)

Use radical notation to write the expression. Simplify if possible. - (2x+2)2/3( 2 x + 2 ) ^ { 2 / 3 }(2x+2)2/3

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (7+23)(7−23)( 7 + \sqrt [ 3 ] { 2 } ) ( 7 - \sqrt [ 3 ] { 2 } )(7+32​)(7−32​)

Find the distance between the pair of points. - (−2,−2)( - 2 , - 2 )(−2,−2) and (4,2)( 4,2 )(4,2)

Solve. - 5x+4=3x+1+3\sqrt { 5 x + 4 } = \sqrt { 3 x + 1 } + 35x+4​=3x+1​+3

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Find all real square roots of the number. $\frac { 4 } { 121 }$

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - $\sqrt { 618 }$

Write with positive exponents. Simplify if possible. - $( - 64 ) ^ { - 2 / 3 }$

Find the cube root. - $\sqrt [ 3 ] { - 125 x ^ { 36 } y ^ { 12 } }$

Provide an appropriate response. -Find the distance between the points $( - 3 , - 6 )$ and $( 7 , - 1 )$ .

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )$

Perform the indicated operation. Write the result in the form a + bi. - $( 18 - 6 i ) ( 3 + i )$

Perform the indicated operation and simplify. Write the result in the form a + bi. - $- \sqrt { - 292 }$

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 3 } { 2 + 7 i }$

Use radical notation to write the expression. Simplify if possible. - $- 36^{1 / 2}$

Provide an appropriate response. -Find the midpoint of the line segment whose endpoints are $( - 6,4 )$ and $( - 18,14 )$ .

Solve. - $\sqrt { x } - 3 = \sqrt { x - 27 }$

Find the midpoint of the line segment whose endpoints are given. - $( - 9 \sqrt { 6 } , 8 \sqrt { 6 } ) , ( - 4 \sqrt { 6 } , 11 \sqrt { 6 } )$

Perform the indicated operation. Write the result in the form a + bi. - $( 7 + 3 i ) + ( 2 - 3 i )$

Use radical notation to write the expression. Simplify if possible. - $( 2 x + 2 ) ^ { 2 / 3 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( 7 + \sqrt [ 3 ] { 2 } ) ( 7 - \sqrt [ 3 ] { 2 } )$

Find the distance between the pair of points. - $( - 2 , - 2 )$ and $( 4,2 )$

Solve. - $\sqrt { 5 x + 4 } = \sqrt { 3 x + 1 } + 3$