/*! 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 9 Find the indicated roots without... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 9

Find the indicated roots without using a calculator. $$ \sqrt{(-3)^{2}} $$

Short Answer

Expert verified
3

Step by step solution

01

Understand the problem

The given expression is \(\root{}{\big((-3)\big)^{2}}\root{}{}\). The task is to find the square root of \((-3)^{2}\).
02

Compute the square

Calculate the square of \(-3\). Remember that squaring a negative number makes it positive. \(-3 \times -3 = 9\). So, \((-3)^{2} = 9\).
03

Compute the square root

Now, find the square root of 9. The square root of 9 is the number which when multiplied by itself gives 9, and it is 3. Hence, \(\root{}{\big(9\big)} = 3\).

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.

Square Roots
A square root is a special value that, when multiplied by itself, gives the original number. To denote the square root, we use the radical symbol \(\sqrt{}\). For example, \(\sqrt{9}\) means 'the square root of 9'. The value of \(\sqrt{9}\) is 3 because 3 multiplied by 3 equals 9.
Here are some key points to remember about square roots:
  • Positive numbers have two square roots: a positive and a negative root. For instance, \(\sqrt{9}\) is 3, and \(-\sqrt{9}\) is -3.
  • The square root of 0 is 0.
  • Perfect squares are numbers like 1, 4, 9, 16, etc., whose square roots are whole numbers.

Squaring Negative Numbers
Squaring a number means multiplying it by itself. For negative numbers, this results in a positive value.
Let's look at \((-3)^{2}\). When we square -3, we essentially do \(-3 \times -3\).
Recall that multiplying two negative numbers results in a positive number. So, \(-3 \times -3\) equals 9.
  • Squaring negative numbers always results in a positive value.
  • To square a negative number, multiply the number by itself without considering the minus sign twice.

Basic Arithmetic Operations
Understanding basic arithmetic operations is essential for solving math problems. There are four fundamental operations:
  • Addition means combining quantities. Example: 3 + 2 = 5.
  • Subtraction means finding the difference between quantities. Example: 5 - 2 = 3.
  • Multiplication means repeated addition of a number. Example: 4 \(\times\) 3 means 4 added to itself 3 times, which is 12.
  • Division means splitting a number into equal parts. Example: 12 \(\div\) 3 means dividing 12 into 3 equal parts, which is 4.

    • In our problem, we use these operations:
    • Squaring (a form of multiplication): \(-3 \times -3\)
    • Finding the square root (related to division): \(\sqrt{9}\)

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

Geometry State the area of the square with the given side length. Find an equation of the line that passes through the points \((-2,0)\) and $(-6,-6) .

Write each fraction in lowest terms. $$ \frac{140}{196} $$

Without computing the value of each pair of numbers, determine which number is greater. For each problem, explain why. $$3^{-1,600} \text { or } 27^{-500}$$

Challenge Consider \(\sqrt[n]{x}\) a. If \(\sqrt[n]{x}\) is positive, what can you say for sure about \(x ?\) Explain. b. If \(\sqrt[n]{x}\) is negative, what can you say for sure about \(n\) and \(x ?\) Explain.

Geometry State the area of the square with the given side length. side length 22 \(\mathrm{cm}\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.