Exam 10: Rational Exponents, Radicals, and Complex Numbers

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 5 } } { \sqrt [ 3 ] { 7 } }$

(Multiple Choice)

4.8/5

(73)

Question 221

Write in terms of i. - $\sqrt { - 162 }$

(Multiple Choice)

4.9/5

(93)

Question 222

Find the distance between the pair of points. - $( - 3,1 )$ and $( - 7,4 )$

(Multiple Choice)

4.9/5

(85)

Question 223

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

(Multiple Choice)

4.9/5

(81)

Question 224

Write the conjugate of the expression. - $\sqrt { 6 } + y$

(Multiple Choice)

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Question 225

Find the midpoint of the line segment whose endpoints are given. - $( - 9 , - 5 ) , ( 4,2 )$

(Multiple Choice)

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Question 226

Use radical notation to write the expression. Simplify if possible. - $16 ^ { 5 / 4 }$

(Multiple Choice)

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Question 227

Identify the domain and then graph the function. - $f(x)=\sqrt{x}+3$ $Identify the domain and then graph the function. - f(x)=\sqrt{x}+3$

(Multiple Choice)

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Question 228

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 120 } } { \sqrt { 6 } }$

(Multiple Choice)

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Question 229

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\left( \frac { 1 } { 9 } \right) ^ { 1 / 2 }$

(Multiple Choice)

4.7/5

(93)

Question 230

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { 5 \sqrt { x } } { \sqrt { 7 y } }$

(Multiple Choice)

4.9/5

(90)

Question 231

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { 5 x ^ { 2 } } + 7 \sqrt { 80 x ^ { 2 } } - 3 \sqrt { 80 x ^ { 2 } }$

(Multiple Choice)

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(80)

Question 232

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

(Multiple Choice)

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Question 233

Perform the indicated operation. Write the result in the form a + bi. -(5 - 2i) + (-5 + 2i)

(Multiple Choice)

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Question 234

Solve. - $\sqrt { x } - 1 = \sqrt { x - 7 }$

(Multiple Choice)

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(89)

Question 235

Use radical notation to write the expression. Simplify if possible. - $( 7 x ) ^ { 3 / 10 }$

(Multiple Choice)

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(85)

Question 236

Solve. - $x = \sqrt { 22 x - 55 } - 3$

(Multiple Choice)

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(78)

Question 237

Use the properties of exponents to simplify the expression. Write with positive exponents. - $\frac { y ^ { 3 / 4 } } { y ^ { 1 / 4 } }$

(Multiple Choice)

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(70)

Question 238

Rationalize the denominator. Assume that all variables represent positive numbers. - $\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }$

(Multiple Choice)

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(65)

Question 239

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $2 \sqrt { 7 } ( \sqrt { 11 } + \sqrt { 7 } )$

(Multiple Choice)

4.9/5

(77)

Question 240

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 5 } } { \sqrt [ 3 ] { 7 } }$

Write in terms of i. - $\sqrt { - 162 }$

Find the distance between the pair of points. - $( - 3,1 )$ and $( - 7,4 )$

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

Write the conjugate of the expression. - $\sqrt { 6 } + y$

Find the midpoint of the line segment whose endpoints are given. - $( - 9 , - 5 ) , ( 4,2 )$

Use radical notation to write the expression. Simplify if possible. - $16 ^ { 5 / 4 }$

Identify the domain and then graph the function. - $f(x)=\sqrt{x}+3$ $Identify the domain and then graph the function. - f(x)=\sqrt{x}+3$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 120 } } { \sqrt { 6 } }$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\left( \frac { 1 } { 9 } \right) ^ { 1 / 2 }$

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { 5 \sqrt { x } } { \sqrt { 7 y } }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { 5 x ^ { 2 } } + 7 \sqrt { 80 x ^ { 2 } } - 3 \sqrt { 80 x ^ { 2 } }$

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

Perform the indicated operation. Write the result in the form a + bi. -(5 - 2i) + (-5 + 2i)

Solve. - $\sqrt { x } - 1 = \sqrt { x - 7 }$

Use radical notation to write the expression. Simplify if possible. - $( 7 x ) ^ { 3 / 10 }$

Solve. - $x = \sqrt { 22 x - 55 } - 3$

Use the properties of exponents to simplify the expression. Write with positive exponents. - $\frac { y ^ { 3 / 4 } } { y ^ { 1 / 4 } }$

Rationalize the denominator. Assume that all variables represent positive numbers. - $\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $2 \sqrt { 7 } ( \sqrt { 11 } + \sqrt { 7 } )$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Rational Exponents, Radicals, and Complex Numbers

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - 5373\frac { \sqrt [ 3 ] { 5 } } { \sqrt [ 3 ] { 7 } }37​35​​

Write in terms of i. - −162\sqrt { - 162 }−162​

Find the distance between the pair of points. - (−3,1)( - 3,1 )(−3,1) and (−7,4)( - 7,4 )(−7,4)

Solve. - 3x+5=5\sqrt { 3 x + 5 } = 53x+5​=5

Write the conjugate of the expression. - 6+y\sqrt { 6 } + y6​+y

Find the midpoint of the line segment whose endpoints are given. - (−9,−5),(4,2)( - 9 , - 5 ) , ( 4,2 )(−9,−5),(4,2)

Use radical notation to write the expression. Simplify if possible. - 165/416 ^ { 5 / 4 }165/4

Identify the domain and then graph the function. - f(x)=x+3f(x)=\sqrt{x}+3f(x)=x​+3

Simplify the radical expression. Assume that all variables represent positive real numbers. - 1206\frac { \sqrt { 120 } } { \sqrt { 6 } }6​120​​

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - (19)1/2\left( \frac { 1 } { 9 } \right) ^ { 1 / 2 }(91​)1/2

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - 5x7y\frac { 5 \sqrt { x } } { \sqrt { 7 y } }7y​5x​​

Add or subtract. Assume all variables represent positive real numbers. - 5x2+780x2−380x2\sqrt { 5 x ^ { 2 } } + 7 \sqrt { 80 x ^ { 2 } } - 3 \sqrt { 80 x ^ { 2 } }5x2​+780x2​−380x2​

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

Perform the indicated operation. Write the result in the form a + bi. -(5 - 2i) + (-5 + 2i)

Solve. - x−1=x−7\sqrt { x } - 1 = \sqrt { x - 7 }x​−1=x−7​

Use radical notation to write the expression. Simplify if possible. - (7x)3/10( 7 x ) ^ { 3 / 10 }(7x)3/10

Solve. - x=22x−55−3x = \sqrt { 22 x - 55 } - 3x=22x−55​−3

Use the properties of exponents to simplify the expression. Write with positive exponents. - y3/4y1/4\frac { y ^ { 3 / 4 } } { y ^ { 1 / 4 } }y1/4y3/4​

Rationalize the denominator. Assume that all variables represent positive numbers. - x−4x+4\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }x​+4x​−4​

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - 27(11+7)2 \sqrt { 7 } ( \sqrt { 11 } + \sqrt { 7 } )27​(11​+7​)

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 5 } } { \sqrt [ 3 ] { 7 } }$

Write in terms of i. - $\sqrt { - 162 }$

Find the distance between the pair of points. - $( - 3,1 )$ and $( - 7,4 )$

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

Write the conjugate of the expression. - $\sqrt { 6 } + y$

Find the midpoint of the line segment whose endpoints are given. - $( - 9 , - 5 ) , ( 4,2 )$

Use radical notation to write the expression. Simplify if possible. - $16 ^ { 5 / 4 }$

Identify the domain and then graph the function. - $f(x)=\sqrt{x}+3$ $Identify the domain and then graph the function. - f(x)=\sqrt{x}+3$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 120 } } { \sqrt { 6 } }$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\left( \frac { 1 } { 9 } \right) ^ { 1 / 2 }$

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { 5 \sqrt { x } } { \sqrt { 7 y } }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { 5 x ^ { 2 } } + 7 \sqrt { 80 x ^ { 2 } } - 3 \sqrt { 80 x ^ { 2 } }$

Solve. - $\sqrt { x } - 1 = \sqrt { x - 7 }$

Use radical notation to write the expression. Simplify if possible. - $( 7 x ) ^ { 3 / 10 }$

Solve. - $x = \sqrt { 22 x - 55 } - 3$

Use the properties of exponents to simplify the expression. Write with positive exponents. - $\frac { y ^ { 3 / 4 } } { y ^ { 1 / 4 } }$

Rationalize the denominator. Assume that all variables represent positive numbers. - $\frac { \sqrt { x } - 4 } { \sqrt { x } + 4 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $2 \sqrt { 7 } ( \sqrt { 11 } + \sqrt { 7 } )$