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Practice with Real Numbers

Site: Saylor Academy
Course: GKT101: General Knowledge for Teachers – Math
Book: Practice with Real Numbers
Printed by: Guest user
Date: Tuesday, May 13, 2025, 11:07 PM

Description

Complete these exercises and check your answers.

Table of contents

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
Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 License.

Answers

  1. \(6\)

  2. \(8\)

  3. \(3\)

  4. \(10\)

  5. \(-2\)

  6. \(-1\)

  7. ⓐ \(\frac{5}{1}\) ⓑ \(\frac{319}{100}\)

  8. ⓐ \(\frac{-12}{1}\) ⓑ \(\frac{9297}{1000}\)

  9. ⓐ \(0.75, 0.22\overline 3\) ⓑ \(1.39174...\)

  10. ⓐ \(0.4\overline 5, 3.59\) ⓑ \(1.919293...\)

  11. ⓐ irrational ⓑ rational

  12. ⓐ irrational ⓑ rational

  13. ⓐ real number ⓑ not a real number

  14. ⓐ real number ⓑ not a real number

  15. ⓐ \(0,\sqrt{36}, 9\)
    ⓑ \(−8, \sqrt{36}, 9\)
    ⓒ \(−8, 0, \frac{12}{5}, \sqrt{36}, 9\)
    ⓓ \(1.95286…\)
    ⓔ \(−8, 0, 1.95286…, \frac{12}{5}, \sqrt{36}, 9\)

  16. ⓐ none
    ⓑ \(−\sqrt{100}, −7, −1\)
    ⓒ \(−\sqrt{100},−7,−\frac{8}{3},−1, 0.77, 3\frac{1}{4}\)
    ⓓ none
    ⓔ \(−\sqrt{100}, −7, −\frac{8}{3}, −1, 0.77, 3\frac{1}{4}\)