/*! 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 15 Simplify. $$8 \sqrt{y}-10 \sqr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 15

Simplify. $$8 \sqrt{y}-10 \sqrt{y}$$

Short Answer

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

Step by step solution

01

Identify Like Terms

In this expression, \(8 \sqrt{y}\) and \(-10 \sqrt{y}\) are like terms because they both contain the square root of 'y'.
02

Combine Like Terms

As both are like terms, we can combine these by subtracting the coefficients. Here, the coefficients are 8 and -10. So, \(8 \sqrt{y}-10 \sqrt{y} = (8 - 10) \sqrt{y}\)
03

Simplify the Coefficient

Subtract 10 from 8 to get -2. So, the expression simplifies to \(-2 \sqrt{y}\).

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.

Understanding Like Terms
To simplify expressions effectively, it's essential to understand the concept of like terms. Like terms are components of an expression that have the same variable(s) raised to the same power(s). In the example \(8 \sqrt{y} - 10 \sqrt{y}\), both terms have the same square root of 'y', making them like terms. This similarity allows us to focus on their coefficients, which are the numbers in front of the terms. By identifying like terms, you can simplify complex expressions more easily.
  • Like terms must have identical variables and exponents.
  • Only coefficients of like terms can be directly added or subtracted.
  • This simplification process keeps the variable part unchanged.
Recognizing like terms is the first step towards combining them into a simpler form.
Exploring Square Roots
Square roots are an essential mathematical concept dealing with finding a number that, when multiplied by itself, gives the original number. The notation \(\sqrt{y}\) means 'the square root of y'. Square roots can often appear in expressions requiring simplification, like in this exercise.
  • The square root symbol (\(\sqrt{}\)) denotes a number giving a specified original when squared.
  • For non-negative numbers, the square root is always non-negative as well.
  • Expressions with square roots can usually be further combined if terms contain identical roots.
Understanding square roots helps when simplifying expressions, especially when like terms are involved.
Combining Terms for Simplification
Combining terms means taking like terms and merging them into fewer terms or even a single term, leading to simpler expressions. This process involves calculating the sum or difference of the coefficients while keeping the variable part intact. In the expression \(8 \sqrt{y} - 10 \sqrt{y}\):
  • First, identify that both terms are like terms.
  • Subtract the coefficients: \(8 - 10\), resulting in \(-2\).
  • This gives the simplified expression \(-2 \sqrt{y}\).
Combining terms is an effective strategy to make expressions easier to handle and compute, especially in algebraic expressions with several terms. It reduces complexity, making it simpler to understand and work with expressions. Remember, the key is ensuring terms are indeed like terms before combining them.

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. $$\frac{x}{6} \sqrt{72 x y^{5}}+\frac{y}{7} \sqrt{98 x^{3} y^{3}}$$

Simplify. $$\frac{2 \sqrt{3}-\sqrt{6}}{5 \sqrt{3}+2 \sqrt{6}}$$

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

Simplify. $$\sqrt{b}(\sqrt{a}-\sqrt{b})$$

Simplify. $$\sqrt{b^{2}+8 b+16}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.