## Algebra 2 Common Core

Published by Prentice Hall

# Chapter 1 - Expressions, Equations, and Inequalities - 1-2 Properties of Real Numbers - Practice and Problem-Solving Exercises - Page 16: 49

#### Answer

$5\sqrt2 \times 5\sqrt2 \times \sqrt2$ inches or approximately $7.07 \times 7.07 \times 7.07$ inches

#### Work Step by Step

The surface area of a cube is equal to six times the area of one side (or one face). Each side/face of a cube is a square whose area is equal the square of its side length. Thus, if the surface area of a cube-shaped jewelry box is $300$ square inches, then the area of each side/face of the jewelry box is: \begin{align*} &=\frac{300}{6} \\&=50\text{ square inches} \end{align*} If we let $x$= side length of the square, then: \begin{align*} x^2&=50\\ \sqrt{x^2}&=\sqrt{50}\\ x&=\sqrt{25(2)}\\ x&=5\sqrt2\approx 7.07 \text{ inches} \end{align*} Therefore, the dimensions of the jewelry box are : $5\sqrt2 \times 5\sqrt2 \times \sqrt2$ inches or approximately $7.07 \times 7.07 \times 7.07$ inches

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