/*! 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 8 Find each of the following squar... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 8

Find each of the following square roots without using a calculator. $$\sqrt{169}$$

Short Answer

Expert verified
The square root of 169 is 13.

Step by step solution

01

Understand the Square Root

The square root of a number, say \( n \), is a value that, when multiplied by itself, equals \( n \). For example, for \(  6 \), we want to find a number \( x \) such that \( x imes x = 169 \).
02

Recall Perfect Squares

Recall that some numbers are perfect squares, which means they are the product of an integer multiplied by itself. For instance, \( 10 \times 10 = 100 \), \( 11 \times 11 = 121 \), \( 12 \times 12 = 144 \), and \( 13 \times 13 = 169 \).
03

Identify the Square Root

Identify that since \( 13 imes 13 = 169 \), the square root of \( 169 \) must be the number \( 13 \). Thus, \(   13 = 169 \).

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 Perfect Squares
Perfect squares are numbers that result from multiplying an integer by itself. They are fundamental when dealing with square roots.
Recognizing perfect squares can simplify many mathematical problems, especially those that involve finding square roots without a calculator.
  • Examples of perfect squares include 1, 4, 9, 16, 25, 36, and so on.
  • These come from \(1 \times 1, 2 \times 2, 3 \times 3, 4 \times 4, 5 \times 5, 6 \times 6,\) etc.
  • Perfect squares grow more distant from each other as the numbers increase, such as \(144 = 12 \times 12\) and \(169 = 13 \times 13\).
When you know perfect squares, finding square roots becomes simply a matter of knowing these specific products. If you spot that a number is a perfect square, you instantly know its square root.
Basics of Multiplication
Multiplication is one of the fundamental arithmetic operations. When we multiply two numbers, we are essentially adding one number to itself a certain number of times. Understanding this operation is key for grasping how square roots and perfect squares work.
  • For example, if we multiply 2 by 3, it is the same as adding 2 three times: \(2 + 2 + 2 = 6\), hence, \(2 \times 3 = 6\).
  • With perfect squares, multiplication involves the same number repeated: \(13 \times 13 = 169\), simplifying to a more streamlined form: \(13^2\).
  • Through multiplication, we can confirm if a number is a perfect square, as seen in \(13 \times 13 = 169\).
Thus, mastering multiplication is not just about calculating results, but recognizing patterns such as perfect squares, which has large implications in finding square roots.
Understanding Integers
Integers include all whole numbers and their negatives. They are crucial when discussing perfect squares and square roots.
In the context of square roots, we focus on non-negative integers since they lead to perfect squares.
  • Examples of integers are \(-3, 0, 7, 13,\) and \(25\).
  • When we talk about perfect squares like \(169,\) they are indeed integers because they result from \(13 \times 13\).
  • Finding a square root means identifying a non-negative integer that when squared, matches the perfect square, like finding \(13\) for \(169\).
Thus, understanding integers helps in identifying and working with perfect squares and their corresponding square roots effectively.

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

A 50-gram egg contains 0.15 milligram of riboflavin. Write 0.15 in words.

Find each of the following sums and differences. (Add or subtract.) $$4 \frac{27}{100}+6 \frac{3}{10}+7 \frac{123}{1,000}$$

Find each of the following sums and differences. (Add or subtract.) $$5 \frac{1}{10}+6 \frac{2}{100}+7 \frac{3}{1,000}$$

Write each fraction as an equivalent fraction with denominator \(100 .\) $$\frac{3}{5}$$

The Google Earth map shows Yellowstone National Park. There is an average of 2.3 moose per square mile. If there are about \(7,986\) moose in Yellowstone, how many square miles does Yellowstone cover? Round to the nearest square mile. (THE IMAGES CANNOT COPY)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.