Real Numbers Math Example 3

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Example 3

easy
Which of the following are NOT real numbers? −4\sqrt{-4}, −4-\sqrt{4}, −83\sqrt[3]{-8}, 10\frac{1}{0}.

Solution

  1. 1
    −4\sqrt{-4} requires the square root of a negative — this is not a real number (it is complex: 2i2i).
  2. 2
    −4=−2-\sqrt{4} = -2 is real. −83=−2\sqrt[3]{-8} = -2 is real (cube roots of negatives are real).
  3. 3
    10\frac{1}{0} is undefined — division by zero is not a real number.

Answer

−4 and 10 are not real numbers\sqrt{-4} \text{ and } \frac{1}{0} \text{ are not real numbers}
The real number system excludes square roots of negative numbers (those belong to the complex numbers) and undefined expressions. Cube roots of negatives, however, are real because (−2)3=−8(-2)^3 = -8.

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More Real Numbers Examples

Example 1 easy

Classify each number as rational or irrational, and state whether it is a real number: [formula], [f

Example 2 medium

Show that between any two distinct real numbers [formula] and [formula] (with [formula]), there exis

Example 4 medium

Give one example of a real number between [formula] and [formula].

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