/*! 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 59 Find each root, if possible. $... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 59

Find each root, if possible. $$-\sqrt[4]{16}$$

Short Answer

Expert verified
The root of the given expression \(-\sqrt[4]{16}\) is \(-2\).

Step by step solution

01

Identify the expression

The expression we need to evaluate is: \[-\sqrt[4]{16}\]
02

Calculate the fourth root of 16

The fourth root of a number x is the number that, when raised to the power of 4, equals x. In this case, we are looking for the fourth root of 16, which can be written as: \(\sqrt[4]{16}\). To find this, we can think in terms of powers of 2, since 16 is a power of 2: \(2^1 = 2\) \(2^2 = 4\) \(2^3 = 8\) \(2^4 = 16\) As we can see, the fourth root of 16 is 2, since \(2^4 = 16\). So, the expression becomes: \[-(2)\]
03

Evaluate the expression

Now we just need to take the negative of 2, which is simply the opposite of 2 on the number line. So, the final expression is: \[-2\] Therefore, the root of the given expression \(-\sqrt[4]{16}\) is \(-2\).

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 Exponents
Exponents are mathematical symbols representing repeated multiplication. When you see a number such as \(2^3\), it means you multiply the base, which is 2, by itself three times: \(2 \times 2 \times 2 = 8\). Exponents are like a shortcut in math, helping simplify calculations through their compact form.
In the exercise, we specifically deal with the number 16, which can be expressed using exponents as \(2^4\). This means that the base number 2, when multiplied by itself four times, results in 16.
  • Exponents indicate how many times to use the base in a multiplication.
  • For example, \(3^2\) means \(3 \times 3\). It's simply a way to write repeated multiplication without writing it all out.
Exponents are foundational concepts in math, and understanding them aids in tackling more complex topics.
Evaluating Expressions with Roots
Evaluating expressions involving roots is similar to working with exponents, but instead of multiplying, we're doing the reverse鈥攆inding which number, when raised to a particular power, gives the original number. This is called taking the root.
In the example \(-\sqrt[4]{16}\), we're asked to find the fourth root of 16. The fourth root of 16 is a number that raised to the power of 4 equals 16. We deduce that this number is 2 since \(2^4 = 16\).
  • To evaluate an expression involving a root:
  • Consider the root's degree, which is 4 in this example.
  • Identify the base number that would satisfy this condition (here it is 2).
Finally, apply any additional operations, such as the negative sign in this exercise, which flips the result from 2 to -2.
Visualizing Numbers on the Number Line
A number line is a simple, visual tool for understanding numbers and their relationships. It allows us to see numbers in a linear sequence where zero is at the center, positive numbers grow to the right, and negative numbers stretch to the left.
In this exercise, after calculating \(\sqrt[4]{16}\) and finding it to be 2, the additional negative sign requires us to move 2 units left from zero. This gives us -2 on the number line.
  • On a number line:
  • The position of a number reflects its value and sign.
  • Moving right increases value, while moving left decreases it.
Using a number line helps with visualizing changes in value and direction, which is particularly useful when manipulating expressions to understand negative outcomes.

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 completely. $$\frac{36+20 \sqrt{2}}{12}$$

Multiply and simplify. $$\sqrt{\frac{6}{7}} \cdot \sqrt{\frac{7}{3}}$$

Simplify completely. Assume all variables represent positive real numbers. $$\sqrt[3]{d^{6}}$$

Rationalize the denominator of each expression. Assume all variables represent positive real numbers. $$\frac{21}{\sqrt[3]{3}}$$

Rationalize the denominator and simplify completely. Assume the variables represent positive real numbers. $$\frac{\sqrt{32}}{\sqrt{5}-\sqrt{7}}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied 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.