– Week 10 Discussion – Radical Expressions in the Real World

This week, you will start learning about radical expressions. While the term “radical expressions”

may sound mathy, they are used in various real-world scenarios such as calculating the speed of

a tsunami, medication scenarios , and even some real-life time-distance problems.

For this discussion, we will explore one such situation through a problem-solving activity. Pick

one of the two mathematical problems given below and provide a detailed step-by-step solution.

The level of details is part of your grade, as indicated by the points in the problem statements.

Alternatively, are you feeling adventurous? In that case, you are more than welcome to choose

your own mathematical problem involving radical expressions or rational exponents. Make sure

to include the following components in your solution.

1. State the problem clearly in your own words.

2. Show detailed step-by-step solution.

3. Cite your source, if any. Important Note: You do not need to cite a source if you have

picked a scenario from your everyday life or work experience. Otherwise, be sure to cite

your source with complete information (author, title, name of publication, date, URL,

etc.).

Note: NO need to type math equations or explain your steps in words. You can simply work the problem

of your choice on a piece of paper, take a photo of your work and then insert the image, if that is easier for you.

Problem 1

Linda works in the US National Oceanic & Atmospheric Administration. They use computer

software to measure the speed of a tsunami at given depths of the ocean. The speed data helps

them predict when the tsunami would make landfall at specific coastal areas. One day, the

software crashed, forcing Linda and her team to calculate the wave speeds manually. The wave

speed formula is

?????????? = ?9.8??

Where ?? is ocean depth in meters. In this case, the ocean depth was 1000 meters.

i. Part (a). How fast was the tsunami wave (in m/s2

)? Simplify your answer. In other words, do

not round. I’m looking for an exact answer, here. (7 points)

ii. Part (b). Now, round your answer from part (a) to two decimal places. In your own words,

interpret what this means. (3 points)

Problem 2

Brandon is walking home from school. He decides to cut across a rectangular park by walking on

a diagonal path that cuts through the park.

(Here it goes an image that I will attach to the tutor that works with me on this question)

i. Part (a). If the north side of the park is 60 feet and the west side is 80 feet, how long is the

diagonal path? (7 points)

ii. Part (b). How much less does Brandon walk by using the diagonal path than by walking along

the sides of the park? (3 points)