Problem 2: Using Radical Expressions in Architecture
This section demonstrates the practical application of radical expressions in architecture, specifically in calculating the perimeter of a stained-glass window. The problem involves finding the perimeter of a window design composed of small squares with 5-inch sides.
Example: The side of each small square in the stained-glass window design is 5 inches. The problem requires calculating the perimeter of the entire window.
The solution process involves using the Pythagorean theorem to find the diagonal length of the window, which is represented as √50. The perimeter is then calculated and rounded to the nearest tenth of an inch.
Highlight: The final answer for the perimeter of the window is approximately 70.7 inches.
Problem 3: Simplifying Before Adding or Subtracting
This section focuses on the important technique of simplifying radical expressions before performing addition or subtraction operations.
Example: The problem asks to simplify the expression √12 + √75 - √3.
The solution demonstrates how to simplify each radical term individually before combining them. This process involves factoring out perfect square roots and simplifying the remaining terms.
Vocabulary: Simplest form - the most reduced version of a radical expression where no further simplification is possible.
The guide also includes a "Got It?" practice problem for students to apply the learned technique.
Problem 4: Multiplying Binomial Radical Expressions
This section covers the multiplication of binomial radical expressions, a more advanced topic in radical operations.
Example: Two examples are provided: (4 + 2√2)(5 + 4√2) and (3 - √7)(5 + √7).
The solutions show the step-by-step process of multiplying these expressions using the FOIL method (First, Outer, Inner, Last) and then simplifying the resulting terms.
Highlight: The process involves distributing each term of one binomial to both terms of the other, then combining like terms and simplifying radicals.
A "Got It?" practice problem is included for students to reinforce their understanding of multiplying binomial radical expressions.
