Question

question the figure below is a square. find the length of side x in simplest radical form with a rational denominator. answer attempt 1 out of 2 x = submit answer

Explanation:

Step1: Recall the property of a square's diagonal

In a square, if the side length is \(a\), and the diagonal is \(d\), then \(d = a\sqrt{2}\). Here, the side length \(a=\sqrt{8}\).

Step2: Substitute the value of \(a\) into the formula

We know that \(x\) (the diagonal) is related to the side length \(\sqrt{8}\) by the formula \(x=\sqrt{8}\times\sqrt{2}\).
Using the property of square - roots \(\sqrt{m}\times\sqrt{n}=\sqrt{mn}\), we have \(x = \sqrt{8\times2}=\sqrt{16}\).
Since \(\sqrt{16}=4\).

Answer:

\(4\)