/*! 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 15 Evaluate or simplify each expres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 15

Evaluate or simplify each expression. (Assume \(x \geq 0 .)\) $$\sqrt{169}$$

Short Answer

Expert verified
The square root of 169 is 13.

Step by step solution

01

Understand the Problem

The expression requires finding the square root of 169, which is written as \(\text{鈭�169}\). The square root of a number is a value that, when multiplied by itself, gives the original number.
02

Identify the Perfect Square

169 is a perfect square since it can be expressed as the square of an integer. Let鈥檚 find the integer whose square is 169.
03

Find the Square Root

By performing the square root operation, \(\text{鈭�169 = 13}\). This is because 13 \(\times\) 13 = 169.
04

Verify the Solution

Verifying the solution by squaring 13 should give 169. Indeed, \[13 \times 13 = 169\]. Therefore, \(\text{鈭�169 = 13}\).

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 Root
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 169 is written as \(\text{鈭�169}\). Here, we are looking for a number which, when squared (or multiplied by itself), equals 169.
Perfect Square
A perfect square is a number that can be expressed as the product of an integer with itself. In this exercise, 169 is identified as a perfect square because there exists an integer that can be multiplied by itself to obtain 169. Let鈥檚 find this integer.
Integer Multiplication
To find the square root of 169, we look for an integer which, when multiplied by itself, produces 169. Through inspection or using a calculator, we find that 13 is the integer that meets this criterion, because \[13 \times 13 = 169.\]
Verification of Results
After finding the square root, it is important to verify the result. We do this by squaring the obtained integer to check if it results in the original number. In this case, \[13 \times 13 = 169.\]
This confirms that \(\text{鈭�169 = 13}\) is correct.

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

Perform the indicated operations and simplify. $$\frac{3}{2 x}+\frac{5}{x+2}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$4(\sqrt{11}-\sqrt{7})+5(\sqrt{7}-\sqrt{11})$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\frac{\sqrt{8}}{7}+\frac{7}{\sqrt{2}}$$

Reduce to lowest terms. $$\frac{10-\sqrt{24}}{12}$$

Factor the given expression as completely as possible. $$x^{2}+10 x-16$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.