Question 1

Find the length of the third side of the triangle by using the Pythagorean theorem.

Accepted Answer

A)  7 yards 
B)  10 yards 
C)  12 yards 
D)  $\sqrt { 194 } \text { yards }$ 
A)  7 yards 
B)  10 yards 
C)  12 yards 
D)  $\sqrt { 194 } \text { yards }$

Question 2

Identify the real and imaginary parts of the complex number. $\frac { 4 } { 7 }$

Accepted Answer

A)  Real: 0 ; imaginary: $\frac { 4 } { 7 }$ 
B)  Real: $\frac { 4 } { 7 }$; imaginary: $i$ 
C)  Real: 4 ; imaginary: 7 
D)  Real: $\frac { 4 } { 7 }$; imaginary: 0 
A)  Real: 0 ; imaginary: $\frac { 4 } { 7 }$ 
B)  Real: $\frac { 4 } { 7 }$; imaginary: $i$ 
C)  Real: 4 ; imaginary: 7 
D)  Real: $\frac { 4 } { 7 }$; imaginary: 0

Question 3

Solve the radical equation, if possible. $$6 = \sqrt { x ^ { 2 } + 3 } - x$$

Accepted Answer

A)  $\left\{ - \frac { 11 } { 4 } \right\}$ 
B)  $\left\{ \frac { 13 } { 2 } \right\}$ 
C)  $\left\{ \frac { 13 } { 4 } \right\}$ 
D)  \{ \} 
A)  $\left\{ - \frac { 11 } { 4 } \right\}$ 
B)  $\left\{ \frac { 13 } { 2 } \right\}$ 
C)  $\left\{ \frac { 13 } { 4 } \right\}$ 
D)  \{ \}

Question 4

Multiply the radical expressions. $( \sqrt { 7 x - 3 } + 4 ) ^ { 2 }$

Accepted Answer

A)  $7 x + 4 \sqrt { 7 x - 3 } + 13$ 
B)  $7 x + 8 \sqrt { 7 x - 3 } + 13$ 
C)  $7 x + 13$ 
D)  $7 x + 1$ 
A)  $7 x + 4 \sqrt { 7 x - 3 } + 13$ 
B)  $7 x + 8 \sqrt { 7 x - 3 } + 13$ 
C)  $7 x + 13$ 
D)  $7 x + 1$

Question 5

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { - \frac { 125 } { 8 } }$

Accepted Answer

A)  $\frac { 5 } { 2 }$ 
B)  $- \frac { 5 } { 2 }$ 
C)  $\frac { 25 } { 4 }$ 
D)  Not a real number 
A)  $\frac { 5 } { 2 }$ 
B)  $- \frac { 5 } { 2 }$ 
C)  $\frac { 25 } { 4 }$ 
D)  Not a real number

Question 6

Which two radicals are like?

Accepted Answer

A)  $- 7 \sqrt { 3 }$ and $\frac { \sqrt { 3 } } { 5 }$ 
B)  $3 \sqrt { 21 }$ and $- \sqrt [ 3 ] { 21 }$ 
C)  $\sqrt { 3 }$ and $\sqrt { 7 }$ 
D)  $3 \sqrt { 21 }$ and $3 \sqrt { 7 }$ 
A)  $- 7 \sqrt { 3 }$ and $\frac { \sqrt { 3 } } { 5 }$ 
B)  $3 \sqrt { 21 }$ and $- \sqrt [ 3 ] { 21 }$ 
C)  $\sqrt { 3 }$ and $\sqrt { 7 }$ 
D)  $3 \sqrt { 21 }$ and $3 \sqrt { 7 }$

Question 7

Rationalize the denominator and simplify completely. $\sqrt [ 4 ] { \frac { 625 } { 27 } }$

Accepted Answer

A)  $\frac { 5 \sqrt [ 4 ] { 27 } } { 3 }$ 
B)  $\frac { 25 \sqrt [ 4 ] { 3 } } { 3 }$ 
C)  $\frac { 5 \sqrt [ 4 ] { 3 } } { 3 }$ 
D)  $\frac { 25 \sqrt [ 4 ] { 27 } } { 3 }$ 
A)  $\frac { 5 \sqrt [ 4 ] { 27 } } { 3 }$ 
B)  $\frac { 25 \sqrt [ 4 ] { 3 } } { 3 }$ 
C)  $\frac { 5 \sqrt [ 4 ] { 3 } } { 3 }$ 
D)  $\frac { 25 \sqrt [ 4 ] { 27 } } { 3 }$

Question 8

Simplify the expression, if possible. $$\frac { 1 } { 1,000,000 ^ { - 1 / 6 } }$$

Accepted Answer

A)  $- 10$ 
B)  10 
C)  $- \frac { 1 } { 10 }$ 
D)  $\frac { 1 } { 10 }$ 
A)  $- 10$ 
B)  10 
C)  $- \frac { 1 } { 10 }$ 
D)  $\frac { 1 } { 10 }$

Question 9

Simplify the expression, if possible. $144 ^ { 3 / 2 }$

Accepted Answer

A)  216 
B)  1738 
C)  1728 
D)  Not a real number 
A)  216 
B)  1738 
C)  1728 
D)  Not a real number

Question 10

Simplify the expression, if possible. $1296 ^ { 1 / 4 }$

Accepted Answer

A)  $\frac { 1 } { 5184 }$ 
B)  5184 
C)  6 
D)  Not a real number 
A)  $\frac { 1 } { 5184 }$ 
B)  5184 
C)  6 
D)  Not a real number

Question 11

On a certain youth league baseball diamond, the bases are 35 ft apart. Assuming home plate and the three bases form a perfect square, find the exact distance from home plate to second base. Then Round to the nearest tenth of a foot.

Accepted Answer

A)  The distance is $35 \sqrt { 2 } \mathrm { ft }$ or approximately $49.5 \mathrm { ft }$. 
B)  The distance is $\sqrt { 35 } \mathrm { ft }$ or approximately $5.9 \mathrm { ft }$. 
C)  The distance is $2 \sqrt { 35 } \mathrm { ft }$ or approximately $11.8 \mathrm { ft }$. 
D)  The distance is $\sqrt { 70 } \mathrm { ft }$ or approximately $8.4 \mathrm { ft }$. 
A)  The distance is $35 \sqrt { 2 } \mathrm { ft }$ or approximately $49.5 \mathrm { ft }$. 
B)  The distance is $\sqrt { 35 } \mathrm { ft }$ or approximately $5.9 \mathrm { ft }$. 
C)  The distance is $2 \sqrt { 35 } \mathrm { ft }$ or approximately $11.8 \mathrm { ft }$. 
D)  The distance is $\sqrt { 70 } \mathrm { ft }$ or approximately $8.4 \mathrm { ft }$.

Question 12

Evaluate the root without using a calculator or note that root is not a real number. $$\sqrt { - 81 }$$

Accepted Answer

A)  6561 
B)  9 
C)  -9 
D)  Not a real number 
A)  6561 
B)  9 
C)  -9 
D)  Not a real number

Question 13

Simplify the expression. $\sqrt { - 64 } \cdot \sqrt { - 5 }$

Accepted Answer

A)  $8 \sqrt { - 5 }$ 
B)  $- 8 \sqrt { 5 }$ 
C)  $8 \sqrt { 5 }$ 
D)  $- 40$ 
A)  $8 \sqrt { - 5 }$ 
B)  $- 8 \sqrt { 5 }$ 
C)  $8 \sqrt { 5 }$ 
D)  $- 40$

Question 14

Rationalize the denominator. $\frac { 2 } { \sqrt { 17 } }$

Accepted Answer

A)  $\frac { 2 \sqrt { 17 } } { 17 }$ 
B)  $\frac { 17 \sqrt { 17 } } { 2 }$ 
C)  $\frac { 4 } { 17 }$ 
D)  Already rationalized 
A)  $\frac { 2 \sqrt { 17 } } { 17 }$ 
B)  $\frac { 17 \sqrt { 17 } } { 2 }$ 
C)  $\frac { 4 } { 17 }$ 
D)  Already rationalized

Question 15

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { 18 z t ^ { 11 } }$

Accepted Answer

A)  $9 t ^ { 5 } \sqrt { 2 z t }$ 
B)  $3 z t ^ { 5 } \sqrt { 6 } t$ 
C)  $3 t \sqrt { 2 z t ^ { 9 } }$ 
D)  $3 t ^ { 5 } \sqrt { 2 z t }$ 
A)  $9 t ^ { 5 } \sqrt { 2 z t }$ 
B)  $3 z t ^ { 5 } \sqrt { 6 } t$ 
C)  $3 t \sqrt { 2 z t ^ { 9 } }$ 
D)  $3 t ^ { 5 } \sqrt { 2 z t }$

Question 16

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. $\sqrt { \frac { 18 b ^ { 8 } } { 2 b ^ { 18 } } }$

Accepted Answer

A)  $\frac { 3 } { b ^ { 5 } }$ 
B)  $\frac { 3 } { b \sqrt { b ^ { 8 } } }$ 
C)  $\sqrt { \frac { 9 } { b ^ { 10 } } }$ 
D)  $3 \sqrt { b ^ { 10 } }$ 
A)  $\frac { 3 } { b ^ { 5 } }$ 
B)  $\frac { 3 } { b \sqrt { b ^ { 8 } } }$ 
C)  $\sqrt { \frac { 9 } { b ^ { 10 } } }$ 
D)  $3 \sqrt { b ^ { 10 } }$

Question 17

Solve the radical equation, if possible. $$\sqrt { 3 x - 3 } + 1 = \sqrt { 3 x + 6 }$$

Accepted Answer

The answer of Solve the radical equation, if possible. \[\sqrt...

Question 18

Simplify. $$i ^ { 20 }$$

Accepted Answer

A)  -1 
B)  1 
C)  i 
D)  -i 
A)  -1 
B)  1 
C)  i 
D)  -i

Question 19

Add. Write the answer in the form a + bi. $$( - 19 - 5 i ) + ( 3 + 10 i )$$

Accepted Answer

A)  $22 + 15 i$ 
B)  $- 16 + 5 i$ 
C)  $- 11 i$ 
D)  $- 11$ 
A)  $22 + 15 i$ 
B)  $- 16 + 5 i$ 
C)  $- 11 i$ 
D)  $- 11$

Question 20

Convert the expression to radical notation. $x ^ { 1 / 5 }$

Accepted Answer

A)  $\frac { \sqrt { x } } { 5 }$ 
B)  $5 \sqrt { x }$ 
C)  $\frac { 1 } { \sqrt { x ^ { 5 } } }$ 
D)  $\sqrt [ 5 ] { x }$ 
A)  $\frac { \sqrt { x } } { 5 }$ 
B)  $5 \sqrt { x }$ 
C)  $\frac { 1 } { \sqrt { x ^ { 5 } } }$ 
D)  $\sqrt [ 5 ] { x }$

Find the length of the third side of the triangle by using the Pythagorean theorem.

Identify the real and imaginary parts of the complex number. $\frac { 4 } { 7 }$

Solve the radical equation, if possible. $6 = \sqrt { x ^ { 2 } + 3 } - x$

Multiply the radical expressions. $( \sqrt { 7 x - 3 } + 4 ) ^ { 2 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { - \frac { 125 } { 8 } }$

Which two radicals are like?

Rationalize the denominator and simplify completely. $\sqrt [ 4 ] { \frac { 625 } { 27 } }$

Simplify the expression, if possible. $\frac { 1 } { 1,000,000 ^ { - 1 / 6 } }$

Simplify the expression, if possible. $144 ^ { 3 / 2 }$

Simplify the expression, if possible. $1296 ^ { 1 / 4 }$

On a certain youth league baseball diamond, the bases are 35 ft apart. Assuming home plate and the three bases form a perfect square, find the exact distance from home plate to second base. Then Round to the nearest tenth of a foot.

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { - 81 }$

Simplify the expression. $\sqrt { - 64 } \cdot \sqrt { - 5 }$

Rationalize the denominator. $\frac { 2 } { \sqrt { 17 } }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { 18 z t ^ { 11 } }$

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. $\sqrt { \frac { 18 b ^ { 8 } } { 2 b ^ { 18 } } }$

Solve the radical equation, if possible. $\sqrt { 3 x - 3 } + 1 = \sqrt { 3 x + 6 }$

Simplify. $i ^ { 20 }$

Add. Write the answer in the form a + bi. $( - 19 - 5 i ) + ( 3 + 10 i )$

Convert the expression to radical notation. $x ^ { 1 / 5 }$

Linear Equations and Inequalities in One Variable

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Exam 6: Radicals and Complex Numbers

Find the length of the third side of the triangle by using the Pythagorean theorem.

Identify the real and imaginary parts of the complex number. 47\frac { 4 } { 7 }74​

Solve the radical equation, if possible. 6=x2+3−x6 = \sqrt { x ^ { 2 } + 3 } - x6=x2+3​−x

Multiply the radical expressions. (7x−3+4)2( \sqrt { 7 x - 3 } + 4 ) ^ { 2 }(7x−3​+4)2

Evaluate the root without using a calculator or note that root is not a real number. −12583\sqrt [ 3 ] { - \frac { 125 } { 8 } }3−8125​​

Which two radicals are like?

Rationalize the denominator and simplify completely. 625274\sqrt [ 4 ] { \frac { 625 } { 27 } }427625​​

Simplify the expression, if possible. 11,000,000−1/6\frac { 1 } { 1,000,000 ^ { - 1 / 6 } }1,000,000−1/61​

Simplify the expression, if possible. 1443/2144 ^ { 3 / 2 }1443/2

Simplify the expression, if possible. 12961/41296 ^ { 1 / 4 }12961/4

On a certain youth league baseball diamond, the bases are 35 ft apart. Assuming home plate and the three bases form a perfect square, find the exact distance from home plate to second base. Then Round to the nearest tenth of a foot.

Evaluate the root without using a calculator or note that root is not a real number. −81\sqrt { - 81 }−81​

Simplify the expression. −64⋅−5\sqrt { - 64 } \cdot \sqrt { - 5 }−64​⋅−5​

Rationalize the denominator. 217\frac { 2 } { \sqrt { 17 } }17​2​

Simplify the radical. Assume that all variables represent positive real numbers. 18zt11\sqrt { 18 z t ^ { 11 } }18zt11​

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. 18b82b18\sqrt { \frac { 18 b ^ { 8 } } { 2 b ^ { 18 } } }2b1818b8​​

Solve the radical equation, if possible. 3x−3+1=3x+6\sqrt { 3 x - 3 } + 1 = \sqrt { 3 x + 6 }3x−3​+1=3x+6​

Simplify. i20i ^ { 20 }i20

Add. Write the answer in the form a + bi. (−19−5i)+(3+10i)( - 19 - 5 i ) + ( 3 + 10 i )(−19−5i)+(3+10i)

Convert the expression to radical notation. x1/5x ^ { 1 / 5 }x1/5

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Quadratic Equations, Functions and Inequalities

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Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Identify the real and imaginary parts of the complex number. $\frac { 4 } { 7 }$

Solve the radical equation, if possible. $6 = \sqrt { x ^ { 2 } + 3 } - x$

Multiply the radical expressions. $( \sqrt { 7 x - 3 } + 4 ) ^ { 2 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { - \frac { 125 } { 8 } }$

Rationalize the denominator and simplify completely. $\sqrt [ 4 ] { \frac { 625 } { 27 } }$

Simplify the expression, if possible. $\frac { 1 } { 1,000,000 ^ { - 1 / 6 } }$

Simplify the expression, if possible. $144 ^ { 3 / 2 }$

Simplify the expression, if possible. $1296 ^ { 1 / 4 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { - 81 }$

Simplify the expression. $\sqrt { - 64 } \cdot \sqrt { - 5 }$

Rationalize the denominator. $\frac { 2 } { \sqrt { 17 } }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { 18 z t ^ { 11 } }$

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. $\sqrt { \frac { 18 b ^ { 8 } } { 2 b ^ { 18 } } }$

Solve the radical equation, if possible. $\sqrt { 3 x - 3 } + 1 = \sqrt { 3 x + 6 }$

Simplify. $i ^ { 20 }$

Add. Write the answer in the form a + bi. $( - 19 - 5 i ) + ( 3 + 10 i )$

Convert the expression to radical notation. $x ^ { 1 / 5 }$