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Simplifying Radical Expressions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=sq

Simplify.
1.  
   6 2
 =
2.  
   7 2
 =

Complexity=1, Mode=int

Simplify.
1.  
√81 =    
2.  
√36 =    

Complexity=1, Mode=alg

Simplify. Assume all variables are nonnegative.
Write exponents with ^. Example: x2 as x^2
1.  
   75x 11
 =    
2.  
   81x 5
 =    

Answers

Complexity=1, Mode=sq

Simplify.
#Correct AnswerYour Answer
1
   6 2
 =
#Correct AnswerYour Answer
2
   7 2
 =

Complexity=1, Mode=int

Simplify.
#Correct AnswerYour Answer
1
√81 =    
Solution
81 is a perfect square.
√81 =
   9 • 9
=9
#Correct AnswerYour Answer
2
√36 =    
Solution
36 is a perfect square.
√36 =
   6 • 6
=6

Complexity=1, Mode=alg

Simplify. Assume all variables are nonnegative.
Write exponents with ^. Example: x2 as x^2
#Correct AnswerYour Answer
1
   75x 11
 =    
Solution
Identify the perfect square factors of 75x 11.
   75x 11
 =
   25 • (x5)2 • 3x
=
   25
•
   (x5)2
•
   3x
=5•x5•
   3x
=5x5
   3x
#Correct AnswerYour Answer
2
   81x 5
 =    
Solution
Identify the perfect square factors of 81x 5.
   81x 5
 =
   81 • (x2)2 • x
=
   81
•
   (x2)2
•
    x
=9•x2•
    x
=9x2
    x
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