Practice with Real Numbers

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.

7. ⓐ \(5\)  ⓑ \(3.19\)
   
   
8. ⓐ \(−12\) ⓑ \(9.279\)
   

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

9. \(0.75, 0.22\overline 3, 1.39174\)
   
   
10. \(0.4\overline 5, 1.919293…, 3.59\)
    

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

11. ⓐ \(\sqrt{25}\)  ⓑ \(\sqrt{30}\)
    
    
12. ⓐ \(\sqrt{164}\) ⓑ \(\sqrt{169}\)
    

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

13. ⓐ \(-\sqrt{81}\) ⓑ \(-\sqrt{121}\)
    
    
14. ⓐ \(-\sqrt{36}\) ⓑ \(-\sqrt{144}\)
    

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

15. \(−8, 0, 1.95286…, \frac{12}{5}, \sqrt{36}, 9\)
    
    
16. \(−\sqrt{100}, −7, −\frac{8}{3}, −1, 0.77, 3\frac{1}{4}\)

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