/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 Simplify. $$8 \sqrt{2}-3 \sqrt... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 47

Simplify. $$8 \sqrt{2}-3 \sqrt{y}-8 \sqrt{2}$$

Short Answer

Expert verified
The simplified form of the given expression is \(-3 \sqrt{y}\).

Step by step solution

01

Identify Similar Terms

Look for the terms in the expression which are exactly same and cancel out. Here, it's \(8 \sqrt{2}\) and \(-8 \sqrt{2}\)
02

Cancel Out the Terms

The terms \(8 \sqrt{2}\) and \(-8 \sqrt{2}\) cancel each other out as they are exactly the same but with opposite signs.
03

Simplify the Remaining Term

After cancelling out, the remaining term is \(-3 \sqrt{y}\). Therefore, the simplified expression is \(-3 \sqrt{y}\).

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!

Key Concepts

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

Like Terms
When simplifying expressions, understanding the concept of "like terms" is crucial. Like terms are terms in an expression that have identical variable parts raised to the same power. They can be combined through addition or subtraction to simplify expressions.

For example:
  • In the example expression, the terms \(8 \sqrt{2}\) and \(-8 \sqrt{2}\) are like terms because they both contain the factor \(\sqrt{2}\).
  • However, \(3 \sqrt{y}\) is not a like term with these because it involves a different variable under the square root.
When simplifying, you combine (add or subtract) like terms to reduce the expression to its simplest form. Identifying and handling like terms properly is a basic and essential skill in algebra.
Radical Expressions
Radical expressions include a root symbol, like square roots (\(\sqrt{}\)), cube roots, etc. Simplifying radical expressions often involves identifying and managing like terms that involve radicals.

A key aspect is:
  • Simplifying the numbers under the root if possible.
  • Combining terms that have the same radical part, very similarly to how like terms are combined.
In the provided example, the expression involves radicals, \(8 \sqrt{2}\) and \(-3 \sqrt{y}\).
Knowing how to cancel out or combine like radical expressions simplifies and reduces the expression efficiently. Understanding how to handle radicals is important in algebra because they frequently appear in equations and need to be simplified consistently.
Variable Terms
Variable terms are parts of an algebraic expression that contain variables (letters that stand for numbers). They can be combined or manipulated to simplify expressions or to solve equations.

For example, in our expression, \(-3 \sqrt{y}\) has the variable \(y\) under the radical. This makes it a variable term distinct from other terms like \(8 \sqrt{2}\), which does not contain a variable.

Key points about variable terms:
  • They can be coefficients (numbers multiplying variables).
  • They follow specific rules for algebraic operations, such as addition, subtraction, and distribution.
Understanding and correctly handling variable terms within expressions is essential for accurate simplification and problem-solving in mathematics. Always keep track of the variables involved and ensure you handle them according to algebraic principles.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Simplify. $$\frac{\sqrt{3}}{5-\sqrt{27}}$$

Simplify. $$(1+\sqrt{6})(1-\sqrt{6})$$

Simplify. $$(2-3 \sqrt{7})(5+2 \sqrt{7})$$

Simplify. $$(\sqrt{x}-y)(\sqrt{x}+y)$$

Simplify. $$\frac{3-\sqrt{6}}{5-2 \sqrt{6}}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.