Question

a square has an area of 79 square units. determine its side length. then, determine if the side length is rational or irrational. √79 does not equal a whole number. so, you can estimate its value. between which two whole numbers is the side length, √79 units? √79 units area = 79 units² √79 units is between the whole numbers. 6 and 7 7 and 8 8 and 9 9 and 10 10 and 11

Explanation:

Step1: Recall square - area formula

Let the side - length of the square be \(s\). The area of a square \(A=s^{2}\). Given \(A = 79\), then \(s=\sqrt{79}\).

Step2: Find perfect - square bounds

We know that \(8^{2}=64\) and \(9^{2}=81\). Since \(64<79<81\), we have \(\sqrt{64}<\sqrt{79}<\sqrt{81}\).

Step3: Simplify square - roots

\(\sqrt{64} = 8\) and \(\sqrt{81}=9\), so \(8<\sqrt{79}<9\).

Answer:

C. 8 and 9