Practice Irrational Numbers in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An irrational number is a real number that cannot be expressed as a ratio of two integers ; its decimal expansion goes on forever without repeating any fixed block of digits.
and go on forever without any pattern—you can't write them as a fraction.
Showing a random 20 of 50 problems.
Example 1
challengeProve that is irrational (outline the contradiction).
Example 2
easyIs rational or irrational?
Example 3
hardIs the set of irrationals closed under addition?
Example 4
easyIs rational or irrational?
Example 5
mediumClassify each: , .
Example 6
mediumOrder from least to greatest: .
Example 7
mediumRationalize and classify .
Example 8
mediumOrder from least to greatest: .
Example 9
mediumIs rational or irrational?
Example 10
easyIs rational or irrational?
Example 11
mediumGive an example of an irrational number between and .
Example 12
mediumSimplify and classify it.
Example 13
challengeShow that is a root of a polynomial with integer coefficients; what is its minimal polynomial?
Example 14
easyIs rational or irrational? Explain.
Example 15
easyBetween which two consecutive integers does lie?
Example 16
mediumShow that lies between and , then estimate it to one decimal place.
Example 17
mediumProve that is irrational by contradiction.
Example 18
mediumGive an example of two irrational numbers whose sum is rational.
Example 19
mediumIs rational or irrational?
Example 20
mediumSimplify and state whether it is rational.