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Chapter 8: Problem 11

Simplify. $$8 \sqrt{x}+9 \sqrt{3 y}-6 \sqrt{x}-21 \sqrt{3 y}$$

Short Answer

Expert verified
\( 2 \sqrt{x} - 12 \sqrt{3y} \)

Step by step solution

01

Identify Like Terms

First, identify the like terms in the expression. Like terms have the same radical part. Here, we have terms with \( \sqrt{x} \) and terms with \( \sqrt{3y} \).
02

Combine Like Terms with \( \sqrt{x} \)

Combine the coefficients of the terms that contain \( \sqrt{x} \). The expression has \(8 \sqrt{x} \) and \(-6 \sqrt{x} \). Adding these together: \( 8 \sqrt{x} - 6 \sqrt{x} = 2 \sqrt{x} \).
03

Combine Like Terms with \( \sqrt{3y} \)

Combine the coefficients of the terms that contain \( \sqrt{3y} \). The expression has \(9 \sqrt{3y} \) and \(-21 \sqrt{3y} \). Adding these together: \( 9 \sqrt{3y} - 21 \sqrt{3y} = -12 \sqrt{3y} \).
04

Write the Simplified Expression

Combine the results from the previous steps to form the simplified expression: \( 2 \sqrt{x} - 12 \sqrt{3y} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Like Terms
When simplifying radical expressions, the first thing to do is to identify like terms. Like terms are terms that have the same radical part. In simpler words, they have the same number under the square root (or any other root) symbol. For example, in the expression \( 8 \sqrt{x} + 9 \sqrt{3y} - 6 \sqrt{x} - 21 \sqrt{3y} \), \( \sqrt{x} \) and \( \sqrt{3y} \) are the radical parts.

When identifying like terms, do not worry about the coefficients (the numbers outside the radical). Just focus on the square root parts. Group together the terms that have the same radical. This will help make the next steps easier. In our example:
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