Exam 9: Radical Expressions and Equations

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -What value of $x$ will make the following equation true? Explain your answer. $\sqrt { 4 x - 2 } + \sqrt { - 8 x + 4 } = 0$

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Question 1

Correct Answer:

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$x = \frac { 1 } { 2 }$ . Since neither square root can have a value less than 0 , both must equal 0 for their sum to be 0. For a square root to equal 0, its radicand must also equal 0 . Thus, $4 x - 2 = - 8 x + 4 = 0$ , which yields the solution $x = \frac { 1 } { 2 }$ . (Explanations will vary.)

Multiply. - $\sqrt { - 3 } \cdot \sqrt { - 3 }$

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Question 2

Correct Answer:

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A

Write the word or phrase that best completes each statement or answers the question. -Find two imaginary numbers whose product is -152.

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Question 3

Correct Answer:

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Answers may vary. One correct answer is 8i and 19i.

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt { x ^ { 2 } + 2 x + 1 } ;$ find $f ( 4 )$

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Question 4

Approximate to the nearest thousandth, using a calculator. - $\sqrt { 2.33 }$

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Question 5

Rationalize the denominator and simplify. - $\frac { 9 \sqrt { 3 } + \sqrt { 11 } } { 7 \sqrt { 3 } + \sqrt { 13 } }$

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Question 6

Provide an appropriate response. -How many real square roots does any negative number have?

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Question 7

Add or subtract. - $5 \sqrt { 245 } - 4 \sqrt { 28 } - \sqrt { 605 } - 2 \sqrt { 63 }$

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Question 8

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $- \sqrt { 175 }$

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Question 9

Simplify the radical expression. Indicate if the expression is not a real number. - $- \sqrt { 529 }$

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Question 10

Provide an appropriate response. - $\sqrt [ 3 ] { 2 } \cdot \sqrt [ 4 ] { 12 }$

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Question 11

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt [ 3 ] { 16 }$

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Question 12

Solve the problem. -The length of the diagonal of a box is given by $\mathrm { D } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$ where L, W, and H are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is 5 ft long, 4 ft high, and 6 ft wide. Give the exact value.

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Question 13

Evaluate the radical function at the given value of the variable. - $f ( x ) = 3 - 5 \sqrt [ 4 ] { 3 t + 12 }$

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Question 14

Divide. - $( 6 - 9 i ) \div ( 5 + 2 i )$

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Question 15

Rationalize the denominator and simplify. - $\frac { \sqrt { 2 } - 7 } { \sqrt { 7 } - 10 }$

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Question 16

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { 196 y ^ { 6 } }$

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Question 17

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { \frac { 4 } { 9 x ^ { 2 } } }$

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Question 18

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $- \sqrt [ 3 ] { - 27 x ^ { 3 } }$

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Question 19

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt { - 121 }$

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Question 20

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -What value of $x$ will make the following equation true? Explain your answer. $\sqrt { 4 x - 2 } + \sqrt { - 8 x + 4 } = 0$

Multiply. - $\sqrt { - 3 } \cdot \sqrt { - 3 }$

Write the word or phrase that best completes each statement or answers the question. -Find two imaginary numbers whose product is -152.

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt { x ^ { 2 } + 2 x + 1 } ;$ find $f ( 4 )$

Approximate to the nearest thousandth, using a calculator. - $\sqrt { 2.33 }$

Rationalize the denominator and simplify. - $\frac { 9 \sqrt { 3 } + \sqrt { 11 } } { 7 \sqrt { 3 } + \sqrt { 13 } }$

Provide an appropriate response. -How many real square roots does any negative number have?

Add or subtract. - $5 \sqrt { 245 } - 4 \sqrt { 28 } - \sqrt { 605 } - 2 \sqrt { 63 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $- \sqrt { 175 }$

Simplify the radical expression. Indicate if the expression is not a real number. - $- \sqrt { 529 }$

Provide an appropriate response. - $\sqrt [ 3 ] { 2 } \cdot \sqrt [ 4 ] { 12 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt [ 3 ] { 16 }$

Evaluate the radical function at the given value of the variable. - $f ( x ) = 3 - 5 \sqrt [ 4 ] { 3 t + 12 }$

Divide. - $( 6 - 9 i ) \div ( 5 + 2 i )$

Rationalize the denominator and simplify. - $\frac { \sqrt { 2 } - 7 } { \sqrt { 7 } - 10 }$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { 196 y ^ { 6 } }$

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { \frac { 4 } { 9 x ^ { 2 } } }$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $- \sqrt [ 3 ] { - 27 x ^ { 3 } }$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt { - 121 }$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Radical Expressions and Equations

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -What value of xxx will make the following equation true? Explain your answer. 4x−2+−8x+4=0\sqrt { 4 x - 2 } + \sqrt { - 8 x + 4 } = 04x−2​+−8x+4​=0

Multiply. - −3⋅−3\sqrt { - 3 } \cdot \sqrt { - 3 }−3​⋅−3​

Write the word or phrase that best completes each statement or answers the question. -Find two imaginary numbers whose product is -152.

Evaluate the radical function at the given value of the variable. - f(x)=x2+2x+1;f ( x ) = \sqrt { x ^ { 2 } + 2 x + 1 } ;f(x)=x2+2x+1​; find f(4)f ( 4 )f(4)

Approximate to the nearest thousandth, using a calculator. - 2.33\sqrt { 2.33 }2.33​

Rationalize the denominator and simplify. - 93+1173+13\frac { 9 \sqrt { 3 } + \sqrt { 11 } } { 7 \sqrt { 3 } + \sqrt { 13 } }73​+13​93​+11​​

Provide an appropriate response. -How many real square roots does any negative number have?

Add or subtract. - 5245−428−605−2635 \sqrt { 245 } - 4 \sqrt { 28 } - \sqrt { 605 } - 2 \sqrt { 63 }5245​−428​−605​−263​

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - −175- \sqrt { 175 }−175​

Simplify the radical expression. Indicate if the expression is not a real number. - −529- \sqrt { 529 }−529​

Provide an appropriate response. - 23⋅124\sqrt [ 3 ] { 2 } \cdot \sqrt [ 4 ] { 12 }32​⋅412​

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - 163\sqrt [ 3 ] { 16 }316​

Evaluate the radical function at the given value of the variable. - f(x)=3−53t+124f ( x ) = 3 - 5 \sqrt [ 4 ] { 3 t + 12 }f(x)=3−543t+12​

Divide. - (6−9i)÷(5+2i)( 6 - 9 i ) \div ( 5 + 2 i )(6−9i)÷(5+2i)

Rationalize the denominator and simplify. - 2−77−10\frac { \sqrt { 2 } - 7 } { \sqrt { 7 } - 10 }7​−102​−7​

Simplify the radical expression. If appropriate, include absolute values. - 196y6\sqrt { 196 y ^ { 6 } }196y6​

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - 49x23\sqrt [ 3 ] { \frac { 4 } { 9 x ^ { 2 } } }39x24​​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - −−27x33- \sqrt [ 3 ] { - 27 x ^ { 3 } }−3−27x3​

Simplify the radical expression. Indicate if the expression is not a real number. - −121\sqrt { - 121 }−121​

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -What value of $x$ will make the following equation true? Explain your answer. $\sqrt { 4 x - 2 } + \sqrt { - 8 x + 4 } = 0$

Multiply. - $\sqrt { - 3 } \cdot \sqrt { - 3 }$

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt { x ^ { 2 } + 2 x + 1 } ;$ find $f ( 4 )$

Approximate to the nearest thousandth, using a calculator. - $\sqrt { 2.33 }$

Rationalize the denominator and simplify. - $\frac { 9 \sqrt { 3 } + \sqrt { 11 } } { 7 \sqrt { 3 } + \sqrt { 13 } }$

Add or subtract. - $5 \sqrt { 245 } - 4 \sqrt { 28 } - \sqrt { 605 } - 2 \sqrt { 63 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $- \sqrt { 175 }$

Simplify the radical expression. Indicate if the expression is not a real number. - $- \sqrt { 529 }$

Provide an appropriate response. - $\sqrt [ 3 ] { 2 } \cdot \sqrt [ 4 ] { 12 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt [ 3 ] { 16 }$

Evaluate the radical function at the given value of the variable. - $f ( x ) = 3 - 5 \sqrt [ 4 ] { 3 t + 12 }$

Divide. - $( 6 - 9 i ) \div ( 5 + 2 i )$

Rationalize the denominator and simplify. - $\frac { \sqrt { 2 } - 7 } { \sqrt { 7 } - 10 }$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { 196 y ^ { 6 } }$

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { \frac { 4 } { 9 x ^ { 2 } } }$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $- \sqrt [ 3 ] { - 27 x ^ { 3 } }$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt { - 121 }$