MATHCP Algebra I  - Unit 23: Operations with Radicals

Definition of a Square Root and Simplifying Radicals


1)

What is the mathematical name for the number under the radical sign?


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2)

Describe how to simplify a radical.


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3)

Explain how to determine when a radical is simplified.


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4)

Describe when absolute value signs are used in simplifying radicals.


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For the next six problems, find the square root. For responses that require non-keyboard symbols, the answer should be expressed in written form as shown in the example below.


5)

Find the square root.


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6)

Find the square root.


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7)

Find the square root.


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8)

Find the square root.


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9)

Find the square root.


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10)

Find the square root.


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11)

Simplify.


12)

Simplify.


13)

Simplify.


Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.
 

Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.

 

Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.

 

Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.


Operations with Radicals

Adding and Subtracting Radicals


14)

Describe how to add or subtract radicals.


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15)

Simplify.


16)

Simplify.


17)

Simplify.


18)

Simplify.


19)

Simplify.


20)

Simplify.


Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.


Multiplying Radicals and Dividing Radicals


21)

What is the process called when eliminating a radical from the denominator? 


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22)

Simplify.


23)

Simplify.


24)

Simplify.


25)

Simplify.


26)

Simplify.


27)

Simplify.


28)

Simplify.


29)

Simplify. Assume all variables are positive numbers.


30)

Simplify. Assume all variables are positive numbers.


31)

Simplify. Assume all variables are positive numbers.


32)

Simplify. Assume all variables are positive numbers.


Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.
 

Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.


Review

Click here to review the unit content explanation for Integers and Equations.


Click here to review the unit content explanation for Rational Numbers and Exponents.


Click here to review the unit content explanation for Linear Equations and Graphs.


Click here to review the unit content explanation for More Systems of Equations.


Click here to review the unit content explanation for Quadratics.


Click here to review the unit content explanation for More on Quadratics.


Click here to review the unit content explanation for Rational Expressions and Functions.


Click here to review the unit content explanation for Rational Expressions.


33)

Solve for “x.”


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34)

Solve the system of equations.


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35)

Identify the vertex of the parabola shown below.


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36)

Write the equation of the line that is perpendicular to 2x – 3y = 9 and contains the point (–6, 12).


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37)

Solve for “x.”


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38)

Add.


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39)

Multiply.


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40)

Solve for “a.


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41)

Simplify.


42)

Find the product of (6x + 1)(3x – 1).


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