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Study Guides > Prealgebra

Introduction to Simplifying and Using Square Roots

A white egg lying on its side on a counter If you drop an egg off a building, how long will it take to hit the ground?
In Mr. Fraser's physics class, the students are doing a messy experiment: They're dropping eggs off the roof of the science building to see how long it takes them to reach the ground. (To minimize cleanup, they've placed tarps down in advance.) Before they conduct the experiment, Mr. Fraser asks the students to list the factors that they think will affect the experiment. Most students think the egg's weight will partially determine how long it takes to hit the ground. But Mr. Fraser proposes that there's actually a simple formula they can use to figure out how long it will take the eggs to reach the ground: the square root of the height the egg is dropped from, divided by [latex]4[/latex]. To find out whether Mr. Fraser is telling the truth, the students will need to simplify expressions with square roots. Read on to find out how to do that.  

Learning Outcomes

By the end of this section, you will be able to:
  • Simplify expressions with square roots
  • Estimate square roots
  • Approximate square roots
  • Simplify variable expressions with square roots
  • Use square roots in applications
 

readiness quiz

Before you get started, take this readiness quiz.
  1. Simplify: [latex]{\left(-9\right)}^{2}[/latex].If you missed this problem, review [link].
  2. Round [latex]3.846[/latex] to the nearest hundredth.If you missed this problem, review [link].
  3. Evaluate [latex]12d[/latex] for [latex]d=80[/latex].If you missed this problem, review [link].

Licenses & Attributions

CC licensed content, Shared previously

  • Egg. Authored by: Lisa Williams. Located at: https://www.flickr.com/photos/pixellou/5923327290/. License: CC BY: Attribution.

CC licensed content, Specific attribution