Math Practice Problems - Simplifying Radical Fractions

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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.

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Complexity=1, Mode=int

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

Complexity=1, Mode=alg

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

Answers

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.

Problem

Correct Answer

Your Answer

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.

Problem

Correct Answer

Your Answer

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.

Problem

Correct Answer

Your Answer

Solution

Simplify under the radical sign

Apply rule for taking the root of a fraction, and simplify

√2

Problem

Correct Answer

Your Answer

Solution

Simplify under the radical sign

Apply rule for taking the root of a fraction, and simplify

√3√2

2√2√2

√3√2

2•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.

Correct Answer

Your Answer

Solution

√x¹⁴

x⁷

Correct Answer

Your Answer

Solution

√x¹

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