# Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises - Page 604: 40

5.7 cm

#### Work Step by Step

As shown in the illustration, the diameter of the smallest circle through which the box will fit is the same length as the diagonal measurement of the box. Use the Pythagorean theorem to find that length. $a^2+b^2=c^2 \longrightarrow$ substitute the side lengths of the box $4^2+4^2=c^2$ find the squares $16+16=c^2 \longrightarrow$ add $32=c^2 \longrightarrow$ find the square root of each side $\sqrt {32}=\sqrt {c^2} \longrightarrow$ simplify $5.7=c$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.