Big Ideas Math: Modeling Real Life, Grade 8
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Exercise 27 Page 419

Is it possible to simplify the real number?

Natural number, whole number, integer, and rational number

Practice makes perfect

Before we consider the given number, let's recall the various types of numbers.

  • Rational Number: A number is a rational number if it can be written in the form ab, where a and b are both integers and b≠ 0.
  • Integer: A number is an integer if it is a positive or negative counting number (or zero). All integers are also rational numbers because any number can be written as a division by one, a1.
  • Whole Number: A number is a whole number if it is a non-negative counting number. All whole numbers are also integers and rational numbers.
    • Natural Number: A number is a natural number if it is a positive counting number. All natural numbers are also whole numbers, integers, and rational numbers.
    • Irrational Number: An irrational number is a number that cannot be written in the form of a rational number. These are recognized as being non-repeating, infinite decimals.
    Let's use these definitions to categorize our real number. sqrt(4) It looks like it is possible to simplify this number, let's try it!
    sqrt(4)
    sqrt(2* 2)
    sqrt(2^2)
    2
    We are left with a positive counting number. Therefore, it is a natural number, whole number, integer, and rational number.