Question

question determine if $sqrt{81}$ is rational or irrational and give a reason for your answer. answer attempt 1 out of 5 the number $sqrt{81}$ is rational because it is a decimal that repeats it is the square root of a non - perfect square it is a decimal that does not repeat or terminate it is the square root of a perfect square it is a decimal that terminates

Explanation:

Step1: Recall the definition of a perfect - square

A perfect - square is a number whose square root is an integer. Since \(9\times9 = 81\), 81 is a perfect - square.

Step2: Recall the definition of a rational number

A rational number is a number that can be expressed as a fraction \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q
eq0\). The square root of a perfect - square is an integer, and an integer can be written as a fraction (e.g., \(9=\frac{9}{1}\)).

Answer:

The number \(\sqrt{81}\) is rational because it is the square root of a perfect square.