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which are rational number

sqrt10 2.339 sqrt5 TT

3 answers

To determine which of the given numbers are rational, let's define what a rational number is. A rational number is any number that can be expressed as the quotient (or fraction) of two integers, where the denominator is not zero.

  1. \(\sqrt{10}\): This is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal expansion is non-terminating and non-repeating.

  2. 2.339: This is a rational number because it can be expressed as a fraction (e.g., \(2.339 = \frac{2339}{1000}\)).

  3. \(\sqrt{5}\): This is also an irrational number for the same reason as \(\sqrt{10}\); it cannot be expressed as a fraction of two integers.

  4. TT: Assuming "TT" is not specified in numerical form, it cannot be classified as a rational number without additional context.

In summary, the only rational number in the list you provided is 2.339.

is -6

a real number, an irrational number, whole number , integer

The number -6 can be classified into several categories:

  1. Real Number: Yes, -6 is a real number. Real numbers include all rational and irrational numbers. Since -6 can be plotted on the number line, it is a real number.

  2. Irrational Number: No, -6 is not an irrational number. Irrational numbers are those that cannot be expressed as a fraction of two integers. Since -6 can be expressed as \(-6 = \frac{-6}{1}\), it is not irrational.

  3. Whole Number: No, -6 is not a whole number. Whole numbers are non-negative integers (0, 1, 2, 3, ...), and since -6 is negative, it does not fit this definition.

  4. Integer: Yes, -6 is an integer. Integers include all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...).

So, to summarize, -6 is a real number and an integer, but it is not a whole number or an irrational number.