/*! 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 90 \(-\sqrt[3]{-343}\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 90

\(-\sqrt[3]{-343}\)

Short Answer

Expert verified
7

Step by step solution

01

Understand the Problem

The task is to simplify the expression \(-\sqrt[3]{-343}\). This involves finding the cube root of \(-343\) and then applying the negative sign.
02

Find the Cube Root

First, determine the cube root of \(-343\). Writing \(-343\) in terms of cubes, remember that \(-343 = -7^3\). Therefore, \(\sqrt[3]{-343} = -7\).
03

Apply the Negative Sign

Now, apply the negative sign outside the cube root, resulting in \(-(-7)\).
04

Simplify the Expression

Simplifying \(-(-7)\) gives \(+7\).

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.

Cube Roots
When you see a cube root, it's like asking: 'What number, when multiplied by itself three times, will give me the original number?' For instance, the cube root of \(-343\) can be found by thinking about which number, when cubed, equals \(-343\).
This leads to \(-7\), because \(-7 \times -7 \times -7 = -343\).
Remember that cube roots can be both positive and negative.
Negative Numbers
Working with negative numbers in algebra can be tricky but gets easier with practice. One important thing to remember is that a negative times a negative equals a positive.
For example, \(-(-7)\) turns into positive \(+7\).
This rule is especially useful when simplifying expressions with negative signs.
Simplification Steps
Simplifying an expression usually means breaking it down into simpler parts. Here's our original problem: \(-\sqrt{ 3 \}{ -343 } \). First, find the cube root of \(-343\) which is \(-7\). Then apply the negative sign in front, leading to \(-(-7)\). Finally, recognize that two negatives make a positive, resulting in \+7\.
Following these steps makes complex problems manageable.

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

Decide whether each expression is equal to \(1,-1, i,\) or \(-i .\) $$ -\sqrt{-1} $$

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \sqrt[3]{x z} \cdot \sqrt{z} $$

Find the equation of a circle satisfying the given conditions. Center: (0,0)\(;\) radius: 12

Simplify. Assume that all variables represent positive real numbers. \(-\sqrt[3]{64 y^{18}}\)

Simplify \(-\sqrt[4]{1250}\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.