• Calculate square roots and apply them in basic operations like addition, subtraction, and rationalizing the denominators.
• Use the product and quotient rules to simplify expressions that include square roots.
• Understand how to use rational exponents in expressions and recognize their connection to roots for simplifying calculations.

Quilt blocks are fabric components sewn together to make a quilt. The quilt block design of a square within a square is called an “economy quilt block.” A textile artist is making a quilt using economy quilt blocks of varying sizes, so he makes a sketch of the design with side length `w` as shown below.

The artist needs to calculate how many square inches of fabric he will need for each orange triangle. First, he will need to determine an expression for the hypotenuse.

*It would help to have the measurements labeled in the diagram.

Photo by Ibrahim Rifath on Unsplash