#### Answer

The number $\sqrt{17}$ is
an irrational number and
a real number.

#### Work Step by Step

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.