/*! 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 76 Approximate. Round to the neares... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 76

Approximate. Round to the nearest thousandth. $$ \sqrt[10]{(1.5)^{6}} $$

Short Answer

Expert verified
1.203

Step by step solution

01

- Simplify the Exponent

Calculate \(1.5^{6}\). Use a calculator to find the value of \(1.5^{6} = 11.390625\).
02

- Take the 10th Root

Find the 10th root of 11.390625. Use a calculator to determine \(\root{10}{11.390625} \).
03

- Approximate and Round

Using a calculator, \( \root{10}{11.390625} \) approximately equals 1.20301. Round this value to the nearest thousandth to get 1.203.

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.

Exponents
Exponents are a way to express repeated multiplication of the same number. For instance, when you see \(1.5^{6}\), it means that you multiply 1.5 by itself six times. Solving such an expression can be tedious by hand, so it's common to use calculators for accurate results.
Here鈥檚 a quick step-by-step on how to handle exponents:
  • Identify the base (in this case, 1.5).
  • Look at the exponent (here it is 6).
  • Multiply the base by itself as many times as the exponent indicates.
So, \(1.5^{6} = 1.5 \times 1.5 \times 1.5 \times 1.5 \times 1.5 \times 1.5 = 11.390625\). Using the exponent rules simplifies complex multiplications. It's an essential tool in algebra and higher-level math.
Roots
Roots are the inverse operation of exponents. The 10th root, denoted as \( \root{10}{...} \) , means finding a number that, when raised to the 10th power, gives the original value. For example, taking the 10th root of 11.390625 means finding a number which, when multiplied by itself 10 times, results in 11.390625.
Unlike exponents, roots can be more complex to solve without a calculator. But the process is straightforward if you follow these steps:
  • Identify the value from which you need to find the root (here it's 11.390625).
  • Determine the root you need (10th root in this problem).
  • Use a calculator or an appropriate mathematical tool to find the root.
When using a calculator, enter 11.390625 and use the root function to find \( \root{10}{11.390625} \). The resultant value is approximately 1.20301.
Approximation and Rounding
Approximation and rounding are essential skills in mathematics to simplify numbers, especially when dealing with long decimals. Rounding helps to make large or complex numbers more manageable and easy to work with.
Here鈥檚 how to round a number to the nearest thousandth:
  • Identify which digit is in the thousandths place (the third digit after the decimal point).
  • Look at the digit immediately to the right of the thousandths place 鈥� this is the ten-thousandths place.
  • If the ten-thousandths digit is 5 or more, round up the thousandths place by adding one to it.
  • If the ten-thousandths digit is less than 5, leave the thousandths place as it is.
For instance, in the value 1.20301, the thousandths place is '3', and the ten-thousandths place is '0'. Since '0' is less than 5, you keep the thousandths place as it is: 1.203. Practicing these steps will improve your precision and simplicity in mathematical calculations.

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

Multiply and simplify. Assume that no radicands were formed by raising negative numbers to even powers. $$ 3 \sqrt{2 x^{5}} \cdot 4 \sqrt{10 x^{2}} $$

f(x)\( and \)g(x)\( are as given. Find \)(f \cdot g)(x) \cdot$ Assume that all variables represent non negativereal numbers. $$f(x)=x+\sqrt{7}, g(x)=x-\sqrt{7}$$

Simplify. $$ \frac{i^{5}+i^{6}+i^{7}+i^{8}}{(1-i)^{4}} $$

Let \(f(x)=x^{2} .\) Find each of the following. $$f(\sqrt{3}-\sqrt{5})$$

Find the midpoint of each segment with the given endpoints. \(\left(\frac{1}{6},-\frac{3}{4}\right)\) and \(\left(-\frac{1}{3}, \frac{5}{6}\right)\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Probability and 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.