McGraw Hill Integrated I, 2012
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McGraw Hill Integrated I, 2012 View details
2. Real Numbers
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Exercise 1 Page P10

Can you simplify the number?

Integers, rationals

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(64) It looks like it is possible to simplify this radical number, so let's do that before we classify it.
    -sqrt(64)
    -sqrt(8* 8)
    -sqrt(8^2)
    -8
    After simplifying, we were left with a negative counting number. Therefore, it is an integer and rational number.