Ch 3: Square Roots

About This Chapter

Learn how to simplify complex expressions that contain a square root, among other related operations, and prepare for the SAT subject exam in mathematics. Video lessons and quizzes help you review how to find a square root in a simple and clear manner.

SAT Mathematics: Square Roots - Chapter Summary

Learn how to estimate a square root and more with the following online video lessons. Lessons in this chapter include:

  • Evaluating square roots of perfect squares
  • Estimating square roots
  • Simplifying square roots when not a perfect square
  • Simplifying complex expressions containing square roots

Our video instructors show you step-by-step how to apply your knowledge of square roots to questions you're likely to find on the SAT mathematics exam. To help you prepare, video lessons include useful features such as self-assessment quizzes and a written transcript.

SAT Mathematics Objectives

The SAT Mathematics Level 1 test is intended to be taken by students who've completed at least three years of college-prep mathematics, including two years of algebra and one of geometry. Students interested in majoring in STEM (science, technology, engineering, and mathematics) and other mathematics-intense degree programs in college might use the math exam to help their applications stand out.

On the exam, you'll answer 50 multiple-choice questions. These questions will cover:

  • Numbers and operations (including elementary number theory, complex numbers, matrices, ratios, and sequences) - 10%-14%
  • Algebra and functions (including equations, functions, expressions, and inequalities) - 38%-42%
  • Geometry and measurement (includes plane Euclidean, 3-dimensional, and coordinate geometry as well as trigonometry) - 38%-42%
  • Data analysis, statistics, and probability (including least squares regression and probability) - 8%-12%

6 Lessons in Chapter 3: Square Roots
Test your knowledge with a 30-question chapter practice test
Evaluating Square Roots of Perfect Squares

1. Evaluating Square Roots of Perfect Squares

Squares and square roots are inverse, or opposite, operations involving radicals. Learn how to determine the square root of perfect squares in this lesson.

Estimating Square Roots

2. Estimating Square Roots

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

Simplifying Square Roots When not a Perfect Square

3. Simplifying Square Roots When not a Perfect Square

Numbers that are imperfect squares are those that, when evaluated, do not give solutions that are integers. The proper mathematical way to simplify these imperfect squares is discussed in this lesson.

Simplifying Expressions Containing Square Roots

4. Simplifying Expressions Containing Square Roots

In order to write radical expressions correctly, they have to be written in their simplest form. This lesson will show you how to simplify expressions containing numbers and variables inside a square root.

Calculating the Square Root of 48: How-To & Steps

5. Calculating the Square Root of 48: How-To & Steps

This lesson will show us how to find the square root of a number 'n' in general, then we will use the general process to find the square root of 48. To finish things up, we'll look at a real world application involving this process.

Calculating the Square Root of 27: How-To & Steps

6. Calculating the Square Root of 27: How-To & Steps

27 isn't a perfect square, so how do we find its root? In this lesson, we will understand an iterative method that uses the basic operations of addition, subtraction, multiplication and division for calculating the square root of 27 and any other number.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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