## Intermediate Algebra: Connecting Concepts through Application

The number $\sqrt{17}$ is an irrational number and a real number.
RECALL: (i) Natural (or Counting) Numbers are $1,2,3,...$ (ii) Whole Numbers are $0,1,2,3,...$ (ii) Integers are $...,−3,−2,−1,0,1,2,3,...$ (iv) Rational Numbers are numbers that can be expressed as a quotient of two integers. (v) Irrational Numbers are numbers that cannot be expressed as a quotient of two integers. (vi) Real Numbers are the set of all rational and irrational numbers, $\sqrt{17}$ cannot be expressed as a quotient of two integers. Thus, the number $\sqrt{17}$ is an irrational number and a real number.