About This Chapter
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%
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.
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.
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.
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.
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.
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.
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Other chapters within the SAT Subject Test Mathematics Level 1: Practice and Study Guide course
- Basic Arithmetic Calculations
- Rational Numbers
- Decimals and Percents
- Basic Algebraic Expressions
- Algebraic Linear Equations & Inequalities
- Algebra: Absolute Value Equations & Inequalities
- Algebra: Polynomials
- Understanding the Basics of Functions
- Algebra: Rational Expressions
- Mathematical Sequences
- Understanding Exponentials & Logarithms
- Complex and Imaginary Numbers
- Coordinate Geometry - Graphing
- Lines and Angles
- Properties of Triangles
- Properties of Circles
- Finding Perimeter, Area & Volume
- Solid Geometry
- Trigonometry Basics
- Understanding Probability & Statistics
- SAT Subject Test Mathematics Level 1 Flashcards