/*! 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 7 Simplify. $$ \sqrt{361} $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 7

Simplify. $$ \sqrt{361} $$

Short Answer

Expert verified
The square root of 361 is 19.

Step by step solution

01

Understanding the Problem

The goal is to simplify the square root of 361. This means we need to determine what number, when squared, equals 361.
02

Recognizing Perfect Squares

A perfect square is a number that can be expressed as the product of an integer with itself. We need to find out if 361 is a perfect square.
03

Finding the Square Root

Check from smaller integers to see which one multiplied by itself equals 361. Through calculation, we find that 19 times 19 equals 361.
04

Conclusion

Since 19 squared is 361, the square root of 361 is 19.

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.

Perfect Squares
Understanding perfect squares is key to simplifying square roots.
A perfect square is an integer that can be formed by multiplying another integer by itself. For example:
  • 1 is a perfect square because 1 * 1 = 1.
  • 16 is a perfect square because 4 * 4 = 16.
  • 25 is a perfect square because 5 * 5 = 25.

Recognizing these perfect squares helps in quickly identifying the square root of a number. In our exercise, you need to determine if 361 is a perfect square.
Square Roots
A square root of a number is a value that, when multiplied by itself, gives the original number.
For any given number 'n', a square root is represented as \( \sqrt{n} \). For example:
  • The square root of 16 is 4, because 4 * 4 = 16.
  • The square root of 25 is 5, because 5 * 5 = 25.
  • The square root of 49 is 7, because 7 * 7 = 49.

In our task, simplifying \( \sqrt{361} \) means finding an integer which, when multiplied by itself, equals 361.
Integer Multiplication
Integer multiplication is fundamental when working with square roots and perfect squares.
The idea is to check successive integers to see if their product results in the given number. For instance:
  • 2 * 2 = 4
  • 3 * 3 = 9
  • 4 * 4 = 16

To simplify \( \sqrt{361} \), we start testing integers to see which one, when multiplied by itself, equals 361. This may involve trial and error until we find that 19 * 19 = 361.
Mathematical Calculations
Mathematical calculations involve a variety of techniques to simplify problems.
When simplifying square roots, performing multiplication checks to verify perfect squares is a common method. In our example, we follow these steps:
  • Identify if 361 is a perfect square.
  • Perform integer multiplication to confirm which number squared gives 361.

Through successive multiplication and verification, we find that 19 multiplied by itself equals 361, thus \( \sqrt{361} = 19 \).
This approach can be applied to other numbers, helping simplify square roots efficiently.

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 approximate to three decimal places. $$ \sqrt{8} $$

Evaluate. $$ 7^{2} $$

A carpenter is to build a fence around a \(9-\mathrm{m}\) by \(12-\mathrm{m}\) garden. a) The posts are to be \(3 \mathrm{~m}\) apart. How many posts will be needed? b) The posts cost \(\$ 8.65\) each. How much will the posts cost? c) The fence will surround all but \(3 \mathrm{~m}\) of the garden, which will be a gate. How long will the fence be? d) The fencing costs \(\$ 3.85\) per meter. What will the cost of the fencing be? e) The gate costs \(\$ 69.95 .\) What is the total cost of the materials?

Complete. \(72 \mathrm{ft}=\) _______ yd.

Interest is compounded semiannually. Find the amount in the account after the given length of time. Round to the nearest cent. $$ \begin{array}{c|c|c|c|} \text { Principal } & \text { Rate of Interest } & \text { Time } & \text { Amount in the Account } \\ \hline \$ 16,100& 5 \% & 20\text { years } & \end{array} $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision 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.