Problem 2 What are the steps for adding or... [FREE SOLUTION]

Chapter 10: Problem 2

What are the steps for adding or subtracting radicals?

Short Answer

Expert verified

To add or subtract radicals, follow these steps: (1) simplify each radical expression by finding prime factors and bringing out pairs/groups of factors; (2) identify like terms, which have the same radicands and types of roots; (3) add or subtract the coefficients of like terms while keeping the radicand the same; and (4) check the result for further simplification if needed. Practice various examples to improve understanding and efficiency in working with radicals.

Step by step solution

Understand the problem

Before adding or subtracting radicals, we need to understand what radicals are and recognize them. A radical is a mathematical expression that includes a root symbol (鈭�), which represents the square root, cube root, or any other higher root of a number or variable.

Simplify the radicals

Before attempting to add or subtract radicals, it's essential to simplify each radical expression. To do this, find the prime factors of the radicand (the number under the root) and try to pair them up for square roots (group of 3 for cube roots, etc.). If a pair (or group) of factors can be brought out of the root, do so and simplify the expression.

Identify like terms

For radicals to be added or subtracted, they must be "like terms." Like terms have the same radicands (number under the root) and the same type (e.g. square root, cube root, etc.). Example: \(3\sqrt{2}\) and \(5\sqrt{2}\) are like terms, while \(2\sqrt{3}\) and \(3\sqrt{2}\) are not.

Add or subtract the like terms

Once the radicals have been simplified and like terms have been identified, we can now proceed by adding or subtracting the radicals. When doing this, simply add or subtract the coefficients in front of the like terms. The radicand remains the same. Example: \(3\sqrt{2} + 5\sqrt{2} = 8\sqrt{2}\)

Check the result

After performing the addition or subtraction, check the result to ensure it is simplified as much as possible. If there's a possibility to simplify further, repeat the steps.

Combining steps

In practice, when faced with an expression requiring the addition or subtraction of multiple radicals, the steps above should be applied systematically, ensuring that all radicals are simplified and like terms are added or subtracted correctly. In some cases, multiple passes through the steps may be required to arrive at the final simplified form of the expression.

Practice with examples

Finally, to solidify understanding of adding or subtracting radicals, practice various examples and problems. This will help in recognizing patterns and improving the ability to simplify and manipulate radical expressions more efficiently.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

What are the steps for adding or subtracting radicals?

Short Answer

Step by step solution

Understand the problem

Simplify the radicals

Identify like terms

Add or subtract the like terms

Check the result

Combining steps

Practice with examples

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Geometry

Pure Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.