Final answer:
The square root of 14 is an irrational number because it cannot be written as a fraction with two integers and its decimal representation is non-terminating and non-repeating.
Step-by-step explanation:
The square root of 14 is indeed an irrational number. An irrational number is a number that cannot be written as a simple fraction, meaning it's a non-terminating, non-repeating decimal. Rational numbers include integers, finite decimals, and fractions where the numerator and denominator are both integers. Since 14 is not a perfect square (there is no integer that can be squared to result in 14), its square root cannot be expressed as a fraction of two integers and therefore is irrational. To demonstrate, the square root of 14 is approximately 3.741657386... with the decimal going on infinitely without repeating. This characteristic defines it as an irrational number.