Practice with Real Numbers

Complete these exercises and check your answers.

Exercises

In the following exercises, simplify.

  1. \sqrt{36}

  2. \sqrt{46}

  3. \sqrt{9}

  4. \sqrt{100}

  5. -\sqrt{4}

  6. -\sqrt{1}


Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercises, write as the ratio of two integers.

  1. ⓐ 5  ⓑ 3.19

  2. ⓐ −12 ⓑ 9.279

In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers

  1. 0.75, 0.22\overline 3, 1.39174

  2. 0.4\overline 5, 1.919293…, 3.59


In the following exercises, identify whether each number is rational or irrational.

  1. ⓐ \sqrt{25}  ⓑ \sqrt{30}

  2. ⓐ \sqrt{164} ⓑ \sqrt{169}


In the following exercises, identify whether each number is a real number or not a real number.

  1. ⓐ -\sqrt{81} ⓑ -\sqrt{121}

  2. ⓐ -\sqrt{36} ⓑ -\sqrt{144}


In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

  1. −8, 0, 1.95286…, \frac{12}{5}, \sqrt{36}, 9

  2. −\sqrt{100}, −7, −\frac{8}{3}, −1, 0.77, 3\frac{1}{4}

Source: Rice University, https://openstax.org/books/elementary-algebra/pages/1-8-the-real-numbers
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