Loading...

## Roots and Powers of Algebraic Expressions## Video Lesson on Radicands and Radical ExpressionsIn this lesson, you'll learn about some common mistakes that students make when working with roots and powers of algebraic expressions on the SAT and how to make sure you don't fall into the same trap. ## Roots and ExponentsWorking with roots and exponents can be tricky at the best of times, but when you start adding in algebraic expressions and factoring, it gets even harder. The bad news is that the test writers on the SAT love to throw in problems that throw students for a loop. But the good news is that by learning how to spot these kinds of problems, you can avoid jumping to the wrong conclusions. In this lesson, you'll learn how to spot two common traps for students working with roots and powers of algebraic expressions. Both of them revolve around distribution properties and order of operations, or the rule that tells us which operation of a given expression to do first. First, we'll go over how these properties work with roots, and then we'll cover how they're applied to exponents. ## Roots and AlgebraRoots of algebraic equations can be tricky. The key is to remember when you can distribute the radical and when you can't. Here's the rule: only distribute the radical when the operation underneath is multiplication or division - never with addition or subtraction. When you have addition or subtraction under the radical sign, you have to do the addition or subtraction before you take the root. The square root of x + y is not the same thing as the square root of x + the square root of y. To illustrate this, let's plug in some real numbers. Let's say x = 16 and y = 9. We'll solve it two ways. On the left is the correct solution and on the right is the incorrect solution. On the left, you first add 16 + 9 to get 25 and then take the square root of that, which is 5. On the right, you can see that if you distribute the radical before doing the addition, you end up with a totally different answer. We can do the same thing with subtraction: again, on the left, you first subtract 25 - 9 to get 16, and then you take the square root of that to get 4. But if you do it wrong and distribute the radical before subtracting, you end up with 2 as your answer. With addition and subtraction, always do the operation underneath the radical before you start worrying about the radical itself. But with multiplication and division, it's different: the square root of x * y is the same thing as the root of x times the root of y. To illustrate this, we'll plug in some numbers: x = 9 and y = 4. On the left, you take 9 * 4 first to get 36 and then take the square root of that to get 6. On the right, you take the square root of 9 times the square root of 4, which is 3 * 2, which is also 6. As you can see, both of these give you the same answer. It works the same way with division: the square root of 9/4 is the same thing as the square root of 9 over the square root of 4. So with addition and subtraction, you can't distribute the radical sign. But with multiplication and division, you can. |

## Powers & AlgebraThe exact same rule holds true for powers. For example, when you square an algebraic equation you can't just distribute the square across addition or subtraction. To make this clear, let's plug in some numbers. We'll use x = 3 and y = 4. On the left is the correct way to do the equation: first add the numbers inside the parentheses and then apply the square. Using this method, we get 49 as the answer. On the right is the wrong way to do it: distributing the square before adding the numbers inside the parentheses. Using this incorrect method, we get 25. That's a pretty big difference! The same is true for subtraction: (x - y)^2 is not the same thing as x^2 - y^2. It's all well and good to add the numbers when you actually have numbers, but what if you have an expression like (x + y)^2? Just factor it: (x + y)^2 = (x + y)(x + y). From there, just use FOIL to get x^2 + 2xy + y^2. And just for the record, it's also worth noting what is equivalent to x^2 - y^2; this is an important equation called the difference of squares. x^2 - y^2 = (x + y)(x - y), not x - y^2. This is a big equation that will show up on the test again, so keep track of it. ## Lesson SummaryIn this lesson, you learned about some common algebraic errors on the SAT and how to avoid them. When you're working with roots and exponents, it's important to know when you can distribute the root or the power and when you can't. In general, you can only distribute with multiplication or division - not addition or subtraction. The SAT will almost certainly give you at least one problem where you'll have to know this, so just be wary of distributing every root and exponent you see. Don't let the search for an easy answer tempt you into a silly mistake! |

What is SAT?
SAT - Structure, Patterns and Scoring
How to Identify Wrong use of Word?
SAT: Identifying Errors in Sentence Structure
SAT Writing and Language Test Words in Context
The SAT Essay
What Is Brainstorming?
SAT - The Five-Paragraph Essay
Sentence Clarity How to Write Clear Sentences
How to Write Well What Makes Writing Good?
How to Identify the Subject of a Sentence
Supporting Details Definition and Examples
How to Proofread an Essay for Spelling and Grammar
SAT Reading Section Structure, Patterns and Scoring
Identifying and Correcting Clause Errors
SAT Reading Passages Types
Analyzing a Literary Passage
Author Purpose: Definition and Examples
The Great Global Conversation Reading Passages on the SAT
Structure of the SAT Math Section Structure, Patterns and Scoring
Radicands and Radical Expressions
Five Main Exponent Properties
What is a Linear Equation
How to Solve a Rational Equation
What is an Inequality?
What is a Function: Basics and Key Terms
How to Solve Quadratics That Are Not in Standard Form
Ratios and Proportions: Definition and Examples
Density: Definition, Formula
Parallel, Perpendicular and Transverse Lines
Properties of Shapes: Triangles
Understanding Bar Graphs and Pie Charts

- NTS GAT - B
- Subject-Verb Agreement: Using Uncommon Singular and Plural Nouns and Pronouns
- Smart GAT Study Plan
- Critical Reasoning
- Synonyms
- How to Crack NTS GAT - B?
- Spellings
- Problems on Trains
- Department of Explosives, MOIP, Government of Pakistan
- The Great Global Conversation Reading Passages on the SAT
- What is a Mathematical Sequence?
- What is a Variable in Algebra?
- Change of speech
- General Knowledge
- Perimeter of Triangles and Rectangles