MathScore EduFighter is one of the best math games on the Internet today. You can start playing for free!

## Simplifying Radical Fractions - 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.

See some of our other supported math practice problems.

### Complexity=1, Mode=sq

Simplify or solve. If a negative answer exists, use a comma (e.g. x=1,-1). If the denominator is 1, leave it blank.

1.
 = 5
x =
2.
 = 7
x =

### Complexity=1, Mode=int

Simplify or solve. If the denominator is 1, leave it blank.

1.
=

2.
=

### Complexity=1, Mode=alg

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

1.

=

2.

=

### Complexity=1, Mode=sq

Simplify or solve. If a negative answer exists, use a comma (e.g. x=1,-1). If the denominator is 1, leave it blank.

1
 = 5
x =
Solution
16 is a square number (42). We're looking for a number x such that, when squared, will be 5*5 times as much as 4*4.
That number x has to be ±5*4 = ±20. You can double check by plugging 4•5 into x in the left side of the original equation:
 = √52 Which of course = 5, the right side of the equation.
2
 = 7
x =
Solution
81 is a square number (92). We're looking for a number x such that, when squared, will be 7*7 times as much as 9*9.
That number x has to be ±7*9 = ±63. You can double check by plugging 9•7 into x in the left side of the original equation:
 = √72 Which of course = 7, the right side of the equation.

### Complexity=1, Mode=int

Simplify or solve. If the denominator is 1, leave it blank.

1
=

Solution
 = Simplify under the radical sign
 = = Apply rule for taking the root of a fraction, and simplify

 = √22

2
=

Solution
 = Simplify under the radical sign
 = = Apply rule for taking the root of a fraction, and simplify

 = √3√22√2√2 = √3√22•2 = Rid the denominator of radicals by multiplying (numerator & denominator) by the radical, and simplify.

### Complexity=1, Mode=alg

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

1

=

Solution
 = =
 = √x14 1 = x 7