/*! 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 662 Simplify. $$ \sqrt{169} $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 662

Simplify. $$ \sqrt{169} $$

Short Answer

Expert verified
\sqrt{169} = 13.

Step by step solution

01

Understand the problem

To simplify the given expression, we need to find the square root of 169.
02

Recall the square root definition

The square root of a number is a value that, when multiplied by itself, gives the original number. Mathematically, if given a number 'x', \(\text{if } a^2 = x, \text{ then } \sqrt{x} = a \).
03

Find the square root

Identify the integer that, when multiplied by itself, equals 169. This integer is 13 because \(\text{since } 13 \times 13 = 169 \).
04

State the simplified form

The simplified form of \(\sqrt{169}\) is 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 definition
The square root is a fundamental concept in mathematics. To understand it, think of a number that produces a specific value when multiplied by itself. For example, when we say the square root of 169, we are looking for a number which, when squared, equals 169. Mathematically, this can be written as: if \( a^2 = x \), then \( \sqrt{x} = a \). In this case, we are solving for \( \sqrt{169} \). The underlying idea is to find a number which reflects our given number through the process of squared multiplication. Hence, understanding this helps simplify expressions encountered in various math problems.
integer multiplication
The process of integer multiplication is simple鈥攊t's the repeated addition of an integer. For this exercise, you multiply the same integer together to confirm the square root. Let's consider this example: finding the square root of 169. We need an integer that, when multiplied by itself, equals 169. This boils down to multiplication tables.
For instance, by checking various numbers:
  • \( 11 \times 11 = 121 \)
  • \( 12 \times 12 = 144 \)
  • \( 13 \times 13 = 169 \)
Clearly, \( 13 \times 13 = 169 \) confirms that 13 is the integer we need. This integer multiplication verifies that the simplified form of \( \sqrt{169} \) is indeed 13.
simplification process
The simplification process in mathematics involves breaking down an expression to its simplest form. To simplify a square root, follow these straightforward steps:
  1. First, understand what you need to simplify. For example, \( \sqrt{169} \)
  2. Next, recall the definition of a square root as the number which, when squared, equals the original number.
  3. Then, find the integer that satisfies this condition. Through integer multiplication, you identify that 13 is the integer because \( 13 \times 13 = 169 \).
  4. Finally, state your simplified answer, which in this case is 13.
This step-by-step method makes the process systematic and easy to follow. Practicing these steps ensures you can handle more complex square root simplifications in the future with confidence.

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

Convert the units. Crista will serve 20 cups of juice at her son's party. Convert the volume to gallons.

Convert the units. A bottle of medicine contained 300 milliliters. Convert this to liters.

Simplify using the distributive property. $$ -(3 x-7) $$

Simplify using the distributive property. $$ r(s-18) $$

Solve. Mireille needs to cut 24 inches of ribbon for each of the 12 girls in her dance class. How many yards of ribbon will she need altogether?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.