Question

The figure below is a square. Find the length of side xx in simplest radical form with a rational denominator.

Answer 1

The length of the square's diagonal, x, when one side is
`\( √(3) \)`, is
`\( √(6) \)` in simplest radical form with a rational denominator.

In a square, the diagonal (x) and one side (given as
`\( √(3) \))` form a right-angled triangle. Using the Pythagorean Theorem:

`\[ x^2 = (\text{side})^2 + (\text{side})^2 \]\[ x^2 = (√(3))^2 + (√(3))^2 \]\[ x^2 = 3 + 3 \]\[ x^2 = 6 \]`

To find x in simplest radical form with a rational denominator, we take the square root of 6:

`\[ x = √(6) \]`

So, the length of side x is
`\( √(6) \)` in simplest radical form with a rational denominator.