Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 34

Chapter 1, Problem 34

In Exercises 33–44, add or subtract terms whenever possible. 8√5+11√5

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Identify the like terms in the expression. Here, both terms contain the square root of 5, so they are like terms: $8\sqrt{5}$ and $11\sqrt{5}$.

Since the terms are like terms, you can add their coefficients (the numbers in front of the square root) together.

Add the coefficients: $8 + 11$ to get the new coefficient for the combined term.

Write the result as the sum of the coefficients multiplied by the common radical: $(8 + 11)\sqrt{5}$.

Simplify the expression by performing the addition inside the parentheses, resulting in a single term with the square root of 5.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Like Terms in Algebra

Like terms are terms that have the same variable parts raised to the same powers. In expressions involving radicals, like terms have the same radicand (the number inside the square root). Only like terms can be added or subtracted by combining their coefficients.

Simplifying Radicals

Simplifying radicals involves expressing the square root in its simplest form by factoring out perfect squares. This helps identify like terms and makes addition or subtraction possible. For example, √5 is already simplified, so terms with √5 can be combined directly.

Adding and Subtracting Radical Expressions

To add or subtract radical expressions, first ensure the radicals are like terms (same radicand). Then, add or subtract their coefficients just like numerical coefficients. For example, 8√5 + 11√5 equals (8 + 11)√5 = 19√5.

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