A straw is placed inside a rectangular box with dimensions 3 inches by 5 inches by 1 inch. The straw fits exactly into the box diagonally from the bottom left corner to the top right back corner. We need to find the length of the straw in simplest radical form.

1. Problem Description

A straw is placed inside a rectangular box with dimensions 3 inches by 5 inches by 1 inch. The straw fits exactly into the box diagonally from the bottom left corner to the top right back corner. We need to find the length of the straw in simplest radical form.

2. Solution Steps

First, we need to find the length of the diagonal of the base of the box. The base has dimensions 3 inches and 5 inches. Let's call the length of the base diagonal $d$. Using the Pythagorean theorem:

$d^2 = 3^2 + 5^2$

$d^2 = 9 + 25$

$d^2 = 34$

$d = \sqrt{34}$

Now, we have a right triangle formed by the base diagonal, the height of the box (1 inch), and the straw. Let's call the length of the straw $s$. We can use the Pythagorean theorem again:

$s^2 = d^2 + 1^2$

$s^2 = (\sqrt{34})^2 + 1^2$

$s^2 = 34 + 1$

$s^2 = 35$

$s = \sqrt{35}$

Since 35 = 5 * 7 and neither 5 nor 7 are perfect squares, $\sqrt{35}$ is already in simplest radical form.

3. Final Answer

$\sqrt{35}$