Question 1

Solve: $\sqrt { 7 x - 6 } + 1 = 7$

Accepted Answer

A)  $\left\{ - \frac { 15 } { 7 } \right\}$ 
B)  $\left\{ \frac { 29 } { 7 } \right\}$ 
C)  $\{ 6 \}$ 
D)  $\left\{ - \frac { 30 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 15 } { 7 } \right\}$ 
B)  $\left\{ \frac { 29 } { 7 } \right\}$ 
C)  $\{ 6 \}$ 
D)  $\left\{ - \frac { 30 } { 7 } \right\}$

Question 2

Multiply. Write the answer in the form $a + b i$ . $- 3 i ( 6 - 6 i )$

Accepted Answer

The answer of Multiply. Write the answer in the form...

Question 3

Simplify the expression. $25 ^ { - \frac { 3 } { 2 } }$

Accepted Answer

A)  125 
B)  -$\frac { 1 } { 125 }$ 
C)  25 
D)  $\frac { 1 } { 125 }$ 
E)  -125 
A)  125 
B)  -$\frac { 1 } { 125 }$ 
C)  25 
D)  $\frac { 1 } { 125 }$ 
E)  -125

Question 4

Simplify the expression. $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 2 } { 3 } }$

Accepted Answer

The answer of Simplify the expression. \(\left( - \frac {...

Question 5

Show that $64 ^ { \frac { 2 } { 6 } }$ is equal to $64 ^ { \frac { 1 } { 3 } }$ .

Accepted Answer

The answer of Show that \(64 ^ { \frac {...

Question 6

Perform the indicated operation. Simplify, if possible. $( 9 \sqrt { 2 } - 7 ) ( 5 \sqrt { 2 } + 4 )$

Accepted Answer

A)  $63 \sqrt { 2 }$ 
B)  $62 + \sqrt { 2 }$ 
C)  62 
D)  $62 + 45 \sqrt { 2 }$ 
A)  $63 \sqrt { 2 }$ 
B)  $62 + \sqrt { 2 }$ 
C)  62 
D)  $62 + 45 \sqrt { 2 }$

Question 7

Simplify the expression. Write the answer without negative exponents. $\frac { 4 ^ { \frac { 1 } { 6 } } 4 ^ { \frac { 2 } { 3 } } } { 4 ^ { \frac { 1 } { 2 } } }$

Accepted Answer

A)  $4 ^ { \frac { 3 } { 2 } }$ 
B)  $\frac { 1 } { 4 ^ { \frac { 2 } { 3 } } }$ 
C)  $4 ^ { \frac { 2 } { 3 } }$ 
D)  $4 ^ { \frac { 1 } { 3 } }$ 
E)  $\frac { 1 } { 4 ^ { \frac { 1 } { 3 } } }$ 
A)  $4 ^ { \frac { 3 } { 2 } }$ 
B)  $\frac { 1 } { 4 ^ { \frac { 2 } { 3 } } }$ 
C)  $4 ^ { \frac { 2 } { 3 } }$ 
D)  $4 ^ { \frac { 1 } { 3 } }$ 
E)  $\frac { 1 } { 4 ^ { \frac { 1 } { 3 } } }$

Question 8

Multiply and simplify, if possible. $3 \sqrt { 5 } \sqrt { 15 }$

Accepted Answer

The answer of Multiply and simplify, if possible. \(3 \sqrt...

Question 9

Express the number in terms of i . $\sqrt { - 49 }$

Accepted Answer

A)  $- 7 \sqrt { i }$ 
B)  -7i 
C)  49i 
D)  7i 
E)  -49i 
A)  $- 7 \sqrt { i }$ 
B)  -7i 
C)  49i 
D)  7i 
E)  -49i

Question 10

A baseball diamond is a square, 90 feet on a side. If the third baseman fields a ground ball 70 feet directly behind third base, how far must he throw the ball to throw a runner out at first base? Find the exact answer. Then give an approximation to two decimal places.

Accepted Answer

A)  $11 \sqrt { 337 } \mathrm { ft } \approx 201.93 \mathrm { ft }$ 
B)  $9 \sqrt { 337 } \mathrm { ft } \approx 165.22 \mathrm { ft }$ 
C)  $11 \sqrt { 337 } \mathrm { ft } \approx 183.58 \mathrm { ft }$ 
D)  $10 \sqrt { 337 } \mathrm { ft } \approx 183.58 \mathrm { ft }$ 
E)  $9 \sqrt { 337 } \mathrm { ft } \approx 183.58 \mathrm { ft }$ 
A)  $11 \sqrt { 337 } \mathrm { ft } \approx 201.93 \mathrm { ft }$ 
B)  $9 \sqrt { 337 } \mathrm { ft } \approx 165.22 \mathrm { ft }$ 
C)  $11 \sqrt { 337 } \mathrm { ft } \approx 183.58 \mathrm { ft }$ 
D)  $10 \sqrt { 337 } \mathrm { ft } \approx 183.58 \mathrm { ft }$ 
E)  $9 \sqrt { 337 } \mathrm { ft } \approx 183.58 \mathrm { ft }$

Question 11

Simplify: $\sqrt [ 3 ] { 48 }$

Accepted Answer

A)  $6 \sqrt [ 3 ] { 2 }$ 
B)  $7 \sqrt [ 3 ] { 6 }$ 
C)  $6 \sqrt [ 3 ] { 6 }$ 
D)  $2 \sqrt [ 3 ] { 6 }$ 
A)  $6 \sqrt [ 3 ] { 2 }$ 
B)  $7 \sqrt [ 3 ] { 6 }$ 
C)  $6 \sqrt [ 3 ] { 6 }$ 
D)  $2 \sqrt [ 3 ] { 6 }$

Question 12

Find the value given that $f ( x ) = \sqrt { x - 1 }$ . $f ( 17 ) = ?$

Accepted Answer

A)  4 
B)  -4 
C)  1 
D)  $- 1$ 
E)  -2 
A)  4 
B)  -4 
C)  1 
D)  $- 1$ 
E)  -2

Question 13

Simplify: $\sqrt [ 3 ] { 81 x ^ { 8 } y ^ { 21 } }$

Accepted Answer

A)  $3 x ^ { 2 } y ^ { 4 } \sqrt [ 3 ] { 3 x ^ { 2 } }$ 
B)  none of these 
C)  $3 x ^ { 2 } y ^ { 7 } \sqrt [ 3 ] { 2 x ^ { 2 } }$ 
D)  $3 x ^ { 2 } y ^ { 7 } \sqrt [ 3 ] { 3 x ^ { 2 } }$ 
A)  $3 x ^ { 2 } y ^ { 4 } \sqrt [ 3 ] { 3 x ^ { 2 } }$ 
B)  none of these 
C)  $3 x ^ { 2 } y ^ { 7 } \sqrt [ 3 ] { 2 x ^ { 2 } }$ 
D)  $3 x ^ { 2 } y ^ { 7 } \sqrt [ 3 ] { 3 x ^ { 2 } }$

Question 14

For right triangle ABC with right angle at C, a = 20 cm and c = 29 cm. Find b .

Accepted Answer

A)  8.5 cm 
B)  9 cm 
C)  21 cm 
D)  38.4 cm 
A)  8.5 cm 
B)  9 cm 
C)  21 cm 
D)  38.4 cm

Question 15

Multiply and simplify, if possible. $\sqrt { 5 } ( 5 \sqrt { 10 } + 4 \sqrt { 7 } )$

Accepted Answer

The answer of Multiply and simplify, if possible. \(\sqrt {...

Question 16

A(n) __________ right triangle is a right triangle with two legs of equal length.

Accepted Answer

The answer of A(n) __________ right triangle is a right...

Question 17

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then __________.

Accepted Answer

A)  $c = a + b$ 
B)  $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ 
C)  $a ^ { 2 } = c + b ^ { 2 }$ 
D)  $b ^ { 2 } = a ^ { 2 } + c ^ { 2 }$ 
E)  $c ^ { 2 } = a ^ { 2 } + b ^ { 2 }$ 
A)  $c = a + b$ 
B)  $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ 
C)  $a ^ { 2 } = c + b ^ { 2 }$ 
D)  $b ^ { 2 } = a ^ { 2 } + c ^ { 2 }$ 
E)  $c ^ { 2 } = a ^ { 2 } + b ^ { 2 }$

Question 18

Simplify: $- \sqrt { - 36 }$

Accepted Answer

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

Question 19

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 x ^ { 12 } y ^ { 3 } }$

Accepted Answer

A)  $2 x ^ { 5 } y \sqrt [ 3 ] { 2 }$ 
B)  $2 x ^ { 4 } y \sqrt [ 3 ] { 2 }$ 
C)  $2 x ^ { 4 } y + \sqrt [ 3 ] { 2 }$ 
D)  $2 x y \sqrt [ 3 ] { 2 x y }$ 
E)  $2 x ^ { 4 } y ^ { 2 } \sqrt [ 3 ] { 2 }$ 
A)  $2 x ^ { 5 } y \sqrt [ 3 ] { 2 }$ 
B)  $2 x ^ { 4 } y \sqrt [ 3 ] { 2 }$ 
C)  $2 x ^ { 4 } y + \sqrt [ 3 ] { 2 }$ 
D)  $2 x y \sqrt [ 3 ] { 2 x y }$ 
E)  $2 x ^ { 4 } y ^ { 2 } \sqrt [ 3 ] { 2 }$

Question 20

For right triangle ABC with right angle at C, a = 2 and c = $2 \sqrt { 2 }$ . Find b .

Accepted Answer

The answer of For right triangle ABC with right angle...

Solve: $\sqrt { 7 x - 6 } + 1 = 7$

Multiply. Write the answer in the form $a + b i$ . $- 3 i ( 6 - 6 i )$

Simplify the expression. $25 ^ { - \frac { 3 } { 2 } }$

Simplify the expression. $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 2 } { 3 } }$

Show that $64 ^ { \frac { 2 } { 6 } }$ is equal to $64 ^ { \frac { 1 } { 3 } }$ .

Perform the indicated operation. Simplify, if possible. $( 9 \sqrt { 2 } - 7 ) ( 5 \sqrt { 2 } + 4 )$

Simplify the expression. Write the answer without negative exponents. $\frac { 4 ^ { \frac { 1 } { 6 } } 4 ^ { \frac { 2 } { 3 } } } { 4 ^ { \frac { 1 } { 2 } } }$

Multiply and simplify, if possible. $3 \sqrt { 5 } \sqrt { 15 }$

Express the number in terms of i . $\sqrt { - 49 }$

A baseball diamond is a square, 90 feet on a side. If the third baseman fields a ground ball 70 feet directly behind third base, how far must he throw the ball to throw a runner out at first base? Find the exact answer. Then give an approximation to two decimal places.

Simplify: $\sqrt [ 3 ] { 48 }$

Find the value given that $f ( x ) = \sqrt { x - 1 }$ . $f ( 17 ) = ?$

Simplify: $\sqrt [ 3 ] { 81 x ^ { 8 } y ^ { 21 } }$

For right triangle ABC with right angle at C, a = 20 cm and c = 29 cm. Find b .

Multiply and simplify, if possible. $\sqrt { 5 } ( 5 \sqrt { 10 } + 4 \sqrt { 7 } )$

A(n) __________ right triangle is a right triangle with two legs of equal length.

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then __________.

Simplify: $- \sqrt { - 36 }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 x ^ { 12 } y ^ { 3 } }$

For right triangle ABC with right angle at C, a = 2 and c = $2 \sqrt { 2 }$ . Find b .

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 7: Radical Expressions and Equations

Solve: 7x−6+1=7\sqrt { 7 x - 6 } + 1 = 77x−6​+1=7

Multiply. Write the answer in the form a+bia + b ia+bi . −3i(6−6i)- 3 i ( 6 - 6 i )−3i(6−6i)

Simplify the expression. 25−3225 ^ { - \frac { 3 } { 2 } }25−23​

Simplify the expression. (−827)−23\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 2 } { 3 } }(−278​)−32​

Show that 642664 ^ { \frac { 2 } { 6 } }6462​ is equal to 641364 ^ { \frac { 1 } { 3 } }6431​ .

Perform the indicated operation. Simplify, if possible. (92−7)(52+4)( 9 \sqrt { 2 } - 7 ) ( 5 \sqrt { 2 } + 4 )(92​−7)(52​+4)

Simplify the expression. Write the answer without negative exponents. 416423412\frac { 4 ^ { \frac { 1 } { 6 } } 4 ^ { \frac { 2 } { 3 } } } { 4 ^ { \frac { 1 } { 2 } } }421​461​432​​

Multiply and simplify, if possible. 35153 \sqrt { 5 } \sqrt { 15 }35​15​

Express the number in terms of i . −49\sqrt { - 49 }−49​

A baseball diamond is a square, 90 feet on a side. If the third baseman fields a ground ball 70 feet directly behind third base, how far must he throw the ball to throw a runner out at first base? Find the exact answer. Then give an approximation to two decimal places.

Simplify: 483\sqrt [ 3 ] { 48 }348​

Find the value given that f(x)=x−1f ( x ) = \sqrt { x - 1 }f(x)=x−1​ . f(17)=?f ( 17 ) = ?f(17)=?

Simplify: 81x8y213\sqrt [ 3 ] { 81 x ^ { 8 } y ^ { 21 } }381x8y21​

For right triangle ABC with right angle at C, a = 20 cm and c = 29 cm. Find b .

Multiply and simplify, if possible. 5(510+47)\sqrt { 5 } ( 5 \sqrt { 10 } + 4 \sqrt { 7 } )5​(510​+47​)

A(n) __________ right triangle is a right triangle with two legs of equal length.

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then __________.

Simplify: −−36- \sqrt { - 36 }−−36​

Simplify the radical expression. All variables represent positive real numbers. 16x12y33\sqrt [ 3 ] { 16 x ^ { 12 } y ^ { 3 } }316x12y3​

For right triangle ABC with right angle at C, a = 2 and c = 222 \sqrt { 2 }22​ . Find b .

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Solve: $\sqrt { 7 x - 6 } + 1 = 7$

Multiply. Write the answer in the form $a + b i$ . $- 3 i ( 6 - 6 i )$

Simplify the expression. $25 ^ { - \frac { 3 } { 2 } }$

Simplify the expression. $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 2 } { 3 } }$

Show that $64 ^ { \frac { 2 } { 6 } }$ is equal to $64 ^ { \frac { 1 } { 3 } }$ .

Perform the indicated operation. Simplify, if possible. $( 9 \sqrt { 2 } - 7 ) ( 5 \sqrt { 2 } + 4 )$

Simplify the expression. Write the answer without negative exponents. $\frac { 4 ^ { \frac { 1 } { 6 } } 4 ^ { \frac { 2 } { 3 } } } { 4 ^ { \frac { 1 } { 2 } } }$

Multiply and simplify, if possible. $3 \sqrt { 5 } \sqrt { 15 }$

Express the number in terms of i . $\sqrt { - 49 }$

Simplify: $\sqrt [ 3 ] { 48 }$

Find the value given that $f ( x ) = \sqrt { x - 1 }$ . $f ( 17 ) = ?$

Simplify: $\sqrt [ 3 ] { 81 x ^ { 8 } y ^ { 21 } }$

Multiply and simplify, if possible. $\sqrt { 5 } ( 5 \sqrt { 10 } + 4 \sqrt { 7 } )$

Simplify: $- \sqrt { - 36 }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 x ^ { 12 } y ^ { 3 } }$

For right triangle ABC with right angle at C, a = 2 and c = $2 \sqrt { 2 }$ . Find b .