/*! 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 32 Evaluate the expression. Give th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 32

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$\sqrt{64}$$

Short Answer

Expert verified
The square root of 64 is 8.

Step by step solution

01

Understanding the Term

Firstly, it鈥檚 important to know what square root means. The square root of a number x is a number that, when multiplied by itself, equals x. In this case, we are looking to find a number which, when multiplied by itself, equals 64.
02

Finding the Square Root of 64

We are solving for \( \sqrt{64} \). The number that multiplies by itself to give 64 is 8. This is because 8*8 equals 64.

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.

Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operations that represent a specific value or set of values. They can include operations like addition, subtraction, multiplication, and division. In the context of evaluating square roots, a mathematical expression such as \(\sqrt{64}\) represents the operation of finding a number which, when squared, will equal 64.
  • The square root symbol \(\sqrt{ }\) is used to denote this operation.
  • A square root expression is often simplified to its most compact form鈥攈ere, simply the number 8.
Expressing values as square roots can be useful in solving equations, understanding geometry, and analyzing data.
Exact Values
When an exercise calls for the 'exact value,' it means that the answer should not be rounded or approximated, but rather the precise answer as a whole number or simplified fraction. An exact value provides the most accurate representation, especially important in algebraic and geometric calculations.
For \(\sqrt{64}\), the exact value is 8, since multiplying 8 by itself gives exactly 64.
  • This avoids possible errors due to rounding.
  • In computational mathematics, having exact values is crucial for precision.
Understanding when and how to find exact values is an essential skill in mathematics, fostering accuracy in problem-solving.
Multiplication
Multiplication is one of the basic arithmetic operations and a fundamental concept in mathematics. It involves calculating the total of one number added together a specified number of times. For example, if we take the number 8:
  • Multiplying 8 by itself means calculating 8 \(\times\) 8.
  • This results in the product of 64.
When it comes to square roots, multiplication helps us verify our results. By multiplying 8 by itself and getting 64, we confirm that 8 is indeed the square root of 64. This demonstrates the close relationship between multiplication and the concept of square roots.
Algebraic Concepts
Algebraic concepts form the backbone of many mathematical principles, and comprehending them can enhance your mathematical intuition. Algebra involves using symbols and letters to represent numbers and quantities in equations and expressions.
In the context of evaluating \(\sqrt{64}\), the application of algebra comes into play:
  • Understanding that \(\sqrt{x}\) refers to finding a number that, when squared, returns x.
  • Using variables to generalize expressions. For example, if \(y = \sqrt{x}\), then \(y^2 = x\).
This approach of breaking down and analyzing expressions and equations helps in solving a wide array of mathematical problems and is a building block for higher-level math like calculus and beyond.

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

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$5 a^{2}+10=20$$

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$4 x^{2}-3=57$$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$6 x^{2}-54=0$$

FINANCIAL ANALYSIS In Exercises 29 and \(30,\) use a graphing calculator and the following information. You are a financial analyst for a software company. You have been asked to project the net profit of your company. The net profit of the company from 1993 to 1998 can be modeled by \(P=6.84 t^{2}-3.76 t+9.29\) where \(P\) is the profit in millions of dollars and \(t\) represents the number of years since \(1993 .\) Use a graphing calculator to estimate how many years it will take for the company's net profit to reach 475 million dollars according to the model.

Use the following information. Scientists simulate a gravity-free environment called microgravity in free- fall situations. A similar microgravity environment can be felt on free-fall rides at amusement parks or when stepping off a high diving platform. The distance \(d\) (in meters) that an object that is dropped falls in \(t\) seconds can be modeled by the equation \(d=\frac{1}{2} g\left(t^{2}\right),\) where \(g\) is the acceleration due to gravity (9.8 meters per second per second). If you want to double the free-fall time, how much do you have to increase the height from which the object was dropped?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure 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.