Question

a square has an area of 79 square units. determine its side length. then, determine if the side is rational or irrational. if the square root of a whole number is equal to a whole number, then it is rational. if the square root of a whole number is not equal to a whole number, then it is irrational. √79 units area = 79 units² √79 is a rational number. √79 is an irrational number.

Explanation:

Step1: Recall area formula for square

The area formula of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 79$, we solve for $s$ by taking the square root of both sides of the equation $79=s^{2}$. So, $s=\sqrt{79}$.

Step2: Determine if the number is rational or irrational

A rational number can be written as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. The square root of a non - perfect square whole number is irrational. Since $79$ is not a perfect square (because there is no whole number $n$ such that $n\times n = 79$), $\sqrt{79}$ is an irrational number.

Answer:

Side - length: $\sqrt{79}$ units; $\sqrt{79}$ is an irrational number.