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Is root 7 a natural number?

Published in Mathematics 1 min read

No, √7 is not a natural number.

Natural Numbers Explained

Natural numbers are positive whole numbers (without fractions or decimals), starting from 1 and continuing infinitely. They are used for counting. Examples of natural numbers include 1, 2, 3, 4, 5, and so on.

Root 7 and Why It's Not a Natural Number

The square root of 7 (√7) is the number that, when multiplied by itself, equals 7. The value of √7 is approximately 2.64575... . This is a non-repeating, non-terminating decimal, which means it is an irrational number. Since √7 is not a whole number, it does not fit the definition of a natural number.

Classification of Numbers

To better understand why √7 is not a natural number, consider the classification of numbers:

  • Natural Numbers: Positive whole numbers (1, 2, 3, ...)
  • Whole Numbers: Natural numbers including zero (0, 1, 2, 3, ...)
  • Integers: Positive and negative whole numbers including zero (..., -2, -1, 0, 1, 2, ...)
  • Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero (e.g., 1/2, -3/4, 5).
  • Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers (e.g., √2, π).
  • Real Numbers: All rational and irrational numbers.

Since √7 cannot be expressed as a fraction of two integers, it's an irrational number and thus, not a natural number.