/*! 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 3 Simplify the expression. $$3 \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 3

Simplify the expression. $$3 \sqrt{5}-\sqrt{5}$$

Short Answer

Expert verified
The simplified expression is \(2\sqrt{5}\).

Step by step solution

01

Identify Like Terms

The terms \(3 \sqrt{5}\) and \(-\sqrt{5}\) are like terms because they both involve the square root of 5. They can be combined because they are similar.
02

Combine Like Terms

Combine the like terms by subtracting \(\sqrt{5}\) from \(3\sqrt{5}\). This gives: \(3\sqrt{5} - \sqrt{5}\) = \(2\sqrt{5}\).

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.

Understanding Like Terms
In algebra, like terms are terms that contain the same variable raised to the same power. This means they can be combined or simplified easily.
In the expression \(3 \sqrt{5} - \sqrt{5}\), the "like" part is due to both terms involving \(\sqrt{5}\).
You can think of like terms as similar items you can group together, like apples with apples.
  • For example, in the expression \(3x - x\), both terms are like terms because they both involve \(x\).
  • Similarly, in \(3\sqrt{5} - \sqrt{5}\), both involve the square root of 5, making them like terms.
By recognizing like terms, you can simplify expressions by adding or subtracting their coefficients. This means you essentially treat \(3\sqrt{5} - \sqrt{5}\) like \(3x - x\), which simplifies to \(2x\).
The trick is just knowing what part of the term makes them alike.
Exploring Square Roots
The square root function is a special mathematical operation that finds a number which, when multiplied by itself, equals the given number. For example, \(\sqrt{9} = 3\) because \(3 \times 3 = 9\).
In the expression \(3\sqrt{5} - \sqrt{5}\), the square root is a component making the terms like terms.
  • Square roots can sometimes be simplified if the number under the root is a perfect square (e.g., \(\sqrt{16} = 4\)).
  • However, \(\sqrt{5}\) will not simplify further as 5 is not a perfect square.
When dealing with square roots in expressions, the key is to focus on combining or simplifying terms that have the same root part.
Additionally, it's important to remember that square roots have properties that are useful in algebraic operations, like how \(\sqrt{a} \times \sqrt{a} = a\).
Mastering Algebraic Operations
Algebraic operations, such as addition, subtraction, multiplication, and division, form the backbone of solving expressions.
In the case of \(3\sqrt{5} - \sqrt{5}\), the operation you perform is subtraction.
  • To perform this subtraction, you subtract the coefficients of like terms: \(3 - 1 = 2\).
  • This gives you the simplified expression \(2\sqrt{5}\).
It's also valuable to recognize the rules for multiplication and division of square root terms in more complex expressions.
This helps in performing operations accurately while respecting the properties of square roots.
Practicing these operations will help build a strong foundation in algebra, empowering you to simplify and solve various types of expressions.

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

Solve the equation. $$2 x+1=\sqrt{9 x}$$

Solve the equation. $$\sqrt{3 t+11}-5 \sqrt{t}=0$$

Use the equation for the velocity of a free-falling object, \(v=\sqrt{2 g h}\), where \(v\) is measured in feet per second, \(g=32\) feet per second squared, and \(h\) is the height (in feet). An object strikes the ground with a velocity of 100 feet per second. Estimate the height from which it was dropped.

Reasoning Square the real number \(3 / \sqrt{2}\). Is this equivalent to rationalizing the denominator? Explain.

Solve the equation. $$\sqrt{6-7 x}=\sqrt{4 x+17}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.