Question

find the length of side $x$ in simplest radical form with a rational denominator.

Explanation:

Step1: Identify triangle type

This is an isosceles right triangle (two equal sides, right angle).

Step2: Apply Pythagorean theorem

For right triangle: $x^2 + x^2 = (\sqrt{6})^2$

Step3: Simplify the equation

$2x^2 = 6$

Step4: Isolate $x^2$

$x^2 = \frac{6}{2} = 3$

Step5: Solve for $x$ (rationalize if needed)

$x = \sqrt{3}$ (already simplest radical form)

Answer:

$\sqrt{3}$