Big Ideas Math: Modeling Real Life, Grade 8
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5. Irrational Numbers
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Exercise 2 Page 402

Can you reduce the square root?

Integer, rational.

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.
    Now, let's try to categorize the given number using these definitions. - sqrt(196) Let's simplify this square root as much as possible.
    - sqrt(196)
    - sqrt(4* 49)
    - sqrt(4)*sqrt(49)
    - sqrt(2*2)*sqrt(49)
    - sqrt(2^2)*sqrt(49)
    - 2*sqrt(49)
    - 2* 7
    - 14
    This is a negative counting number. These numbers fall into two categories, integers and rational numbers.