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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 or solve. When solving for x, make sure to give all possible answers. Example: x = 3, -3

1.
 ( -8) 2
=
2.
 8 2
=

### Complexity=1, Mode=int

Simplify or solve. When solving for x, make sure to give all possible answers. Example: x = 3, -3

1.
 √108 =
2.
 √81 =

### Complexity=1, Mode=alg

Simplify. Assume all variables are nonnegative.
Write exponents with ^. Example: write x2 as x^2.

1.
 27x 3
=
2.
 50x 19
=

### Complexity=1, Mode=sq

Simplify or solve. When solving for x, make sure to give all possible answers. Example: x = 3, -3

1
 ( -8) 2
=
2
 8 2
=

### Complexity=1, Mode=int

Simplify or solve. When solving for x, make sure to give all possible answers. Example: x = 3, -3

1
 √108 =
Solution
Identify the largest perfect square factor of 108:
 √108 = √36 • 3 = √36 • √3 = 6 • √3

If you do not recognize a perfect square, use factoring:

 √108 = √2 • 2 • 3 • 3 • 3

Take out any paired numbers from under the radical sign.
Remember that the square root of something is a number that, when multiplied by itself, would give you back the first number.

2
 √81 =
Solution
81 is a perfect square.
 √81 = √9 • 9 = 9

### Complexity=1, Mode=alg

Simplify. Assume all variables are nonnegative.
Write exponents with ^. Example: write x2 as x^2.

1
 27x 3
=
Solution
Identify the perfect square factors of 27x 3.
 27x 3
=
 9 • x2 • 3x
=9
 x2
3x
=3x3x
=3x√3x
2
 50x 19
=
Solution
Identify the perfect square factors of 50x 19.
 50x 19
=
 25 • (x9)2 • 2x
=25
 (x9)2
2x
=5x92x
=5x92x