/*! 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 84 Use a calculator to approximate ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 84

Use a calculator to approximate each radical to three decimal places. $$ \sqrt[3]{555} $$

Short Answer

Expert verified
The approximate value of \(\root{3}{555}\) to three decimal places is 8.228.

Step by step solution

01

- Understand the Expression

The given expression is the cube root of 555, which is written as \(\root{3}{555}\). We need to approximate this value to three decimal places.
02

- Use a Calculator

To find the cube root, input the number 555 into a scientific calculator and use the cube root function. Depending on the calculator, this might involve pressing a specific root button or raising 555 to the power of \( \frac{1}{3} \).
03

- Record the Result

The calculator will display the approximate value of \(\root{3}{555}\). Make sure to round this result to three decimal places.

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 Root
Finding the cube root of a number is like asking what number, when multiplied by itself three times, gives you the original number. For example, the cube root of 8 is 2 because \(2 \times 2 \times 2 = 8\). In mathematical notation, the cube root of a number X is written as \(\sqrt[3]{X}\) or \(X^{1/3}\). Cube roots can be either positive or negative because both \(2^3 = 8\) and \((-2)^3 = -8\). When approximating cube roots, we often need to use a calculator, especially if the number isn't a perfect cube like 8.
Scientific Calculator
A scientific calculator is a device that can perform a variety of mathematical operations, including finding cube roots. These calculators have special functions that make it easy to find roots. To calculate the cube root of 555:
  • First, turn on your scientific calculator.
  • Look for a button denoted as \(\sqrt[3]{ }\), \(\root{3}{}{ }\), or similar notation. Some calculators might not have this specific function.
  • If your calculator does not have a cube root button, you can use the exponentiation function. Input 555 and press the power button followed by \(\frac{1}{3}\).
Understand your calculator鈥檚 specific method, as this can vary between models.
Decimal Places
When a number is approximated to a certain number of decimal places, it means rounding the number to that many digits after the decimal point for precision. For example, approximating \(3.14159\) to three decimal places gives you \(3.142\). In the context of our exercise:
  • When you calculate the cube root of 555 using your calculator, you might get a long decimal number like \(\root[3]{555} \approx 8.2285935\).
  • To round this to three decimal places, look at the fourth decimal digit (the one right after the third decimal place). If it is 5 or more, round the third decimal up by one.
  • In our example, since the fourth digit is 5, we round up. Thus, \(8.2285935\) approximates to 8.229 when rounded to three decimal places.
Rounding helps in making the number simpler and more manageable, while still maintaining precision within a certain limit.

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

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

Work each problem. Meteorologists can determine the duration of a storm using the function $$T(d)=0.07 d^{3 / 2}$$ where \(d\) is the diameter of the storm in miles and \(T\) is the time in hours. Find the duration of a storm with a diameter of \(16 \mathrm{mi}\). Round the answer to the nearest tenth of an hour.

Simplify each expression. Assume that all variables represent positive real numbers. $$ 6 a^{7 / 4}\left(a^{-7 / 4}+3 a^{-3 / 4}\right) $$

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \sqrt[3]{\sqrt[5]{\sqrt{y}}} $$

Find the distance between each pair of points. \((x+y, y)\) and \((x-y, x)\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

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.