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Radicals Homework -- Radicals (aka* Roots)

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides sample problems which develop concepts related to radicals.

As a student of mine once said, “In real life, no one ever says ‘Here’s 100 dollars, what’s the square root of it?’” She’s right, of course—as far as I know, no one ever takes the square root of money. And she is asking exactly the right question, which is: why do we need roots anyway?

Exercise 1

If a square is 49 ft 2 49 ft 2 in area, how long are the sides?

Q. You call that real life?

A. OK, you asked for it…

Exercise 2

A real estate developer is putting houses down on a plot of land that is 50 acres large. He wants to put down 100 houses, so each house will sit on a 1 2 1 2 -acre lot. (1 acre is 43,560 square feet.) If each house sits on a square lot, how long are the sides of each lot?

Exercise 3

A piano is dropped from a building 100 ft high. (“Dropped” implies that someone just let go of it, instead of throwing it—so it has no initial velocity.)

  • a. Write the equation of motion for this piano, recalling as always that h ( t ) = h o + v o t 16 t 2 h(t)= h o + v o t16 t 2
  • b. According to the equation, how high is the piano when t = 0 t=0? Explain in words what this answer means.
  • c. After 2 seconds, how high is the piano?
  • d. How many seconds does it take the piano to reach the ground?
  • e. Find the inverse function that will enable to me find the time t t when the piano reaches any given height h h.

Convinced? Square roots come up all the time in real life, because squaring things comes up all the time in real life, and the square root is how you get back. So we’re going to have a unit on square roots.

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