/*! 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 662 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 662

In the following exercises, simplify. $$ -\sqrt{25} $$

Short Answer

Expert verified
-5

Step by step solution

01

Evaluate the Square Root

First, find the square root of the number inside the square root symbol. In this case, the inside number is 25. The square root of 25 is 5, because 5 * 5 = 25.
02

Apply the Negative Sign

After finding the square root, apply the negative sign that is in front of the square root symbol. Therefore, we take the positive value 5 from the previous step and apply the negative sign to it, giving us -5.
03

Simplify the Expression

The simplified form of the original expression -鈭�25 is therefore -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.

negative sign
When you see a negative sign in front of a square root, it means you will make the result of the square root negative. It is important to note that the negative sign is not inside the square root. This means you first simplify the square root, and only then apply the negative sign.

For example, in the expression \(-\sqrt{25}\), you first find the square root of 25, which is 5. After you have this result, you'll apply the negative sign, turning it into -5.

Always remember: the simplification of the square root comes first, and the application of the negative sign follows.
  • Step 1: Find the square root.
  • Step 2: Apply the negative sign.
square root
A square root of a number is a value that, when multiplied by itself, gives the original number. The symbol for square root is \( \sqrt{} \).

For instance, \(\sqrt{25} = 5\), because \(5 \times 5 = 25\).

Here are some key points to understand about square roots:
  • The square root of a positive number is positive.
  • The square root of zero is zero.
  • Negative numbers do not have real square roots (however, they do have complex roots!).

In the given exercise, you simplified \(-\sqrt{25}\) by first finding that \(\sqrt{25} = 5\) and then applying the negative sign in the next step.
simplification steps
Simplifying expressions involving square roots can be straightforward if you follow a step-by-step approach.

Let's revisit the steps for simplifying \(-\sqrt{25}\):
  • Step 1: Identify and calculate the square root. Here, find the square root of 25, which is 5.
  • Step 2: Apply any additional operations, like a negative sign, outside the square root symbol. Thus, \(-\sqrt{25} = -5\).

By following these simplification steps, you ensure you are correctly applying mathematical rules.

Remember these steps whenever you simplify similar expressions, and practice with different numbers to build confidence in this method.

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

In the following exercises, order each of the following pairs of numbers, using < or >. $$0.86\underline\quad0.69$$

Jim ran a 100-meter race in 12.32 seconds. Tim ran the same race in 12.3 seconds. Who had the faster time, Jim or Tim? How do you know?

In the following exercises, translate the English phrase into an algebraic expression. 105 calories in \(x\) ounces

Mollie had a 16 -ounce cappuccino at her neighborhood coffee shop. The cappuccino had 110 calories. If Mollie walks for one hour, she burns 246 calories. For how many minutes must Mollie walk to burn off the calories in the cappuccino? Explain your reasoning.

In the following exercises, translate the English phrase into an algebraic expression. \(j\) beats in 0.5 minutes
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

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.