the figure below is a square. find the length of side x in simplest radical form with a rational denominator.

Explanation:

Step1: Recall Pythagorean theorem for square

In a square, if the side - length is (a) and the diagonal is (d), then (d^{2}=a^{2}+a^{2}=2a^{2}) (by Pythagorean theorem, since the two sides of the right - triangle formed by the diagonal and two sides of the square are equal). Here, let the side - length of the square be (\sqrt{8}) and the diagonal be (x). Then (x^{2}=(\sqrt{8})^{2}+(\sqrt{8})^{2}).

Step2: Calculate the value of (x^{2})

[ \begin{align*} x^{2}&=8 + 8\ x^{2}&=16 \end{align*} ]

Step3: Solve for (x)

Take the square root of both sides: (x=\sqrt{16}=4)

Answer:

4