/*! 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 407 Is \(\sqrt{144}\) rational or ir... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 407

Is \(\sqrt{144}\) rational or irrational?

Short Answer

Expert verified
The square root of 144 is rational because it equals 12, an integer.

Step by step solution

01

Understand the Definition

A rational number can be expressed as the quotient of two integers, i.e., \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \) is not zero. An irrational number cannot be expressed this way.
02

Calculate the Square Root

Determine the square root of 144. \( \sqrt{144} = 12 \).
03

Verify the Result

Check if the result is an integer. The square root of 144 is 12, which is an integer.
04

Conclusion

Since 12 can be expressed as \( \frac{12}{1} \), it is a rational number. Thus, \( \sqrt{144} \) is rational.

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 Square Roots
Square roots are numbers that produce a specified number when multiplied by themselves. For instance, the square root of 25 is 5, because 5 multiplied by itself equals 25. Square roots can be whole numbers (perfect squares) or decimals. When a number is a perfect square, like 144, its square root is an integer.
What Are Integers?
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. For example, -3, 0, and 7 are all integers. In our exercise, we calculated the square root of 144 and arrived at 12, which is an integer.
Rational vs Irrational Numbers
Rational numbers can be expressed as a fraction \left( \frac{a}{b} \right) where both \(a\) and \(b\) are integers, and \(b\) is not zero. Examples include 1/2, 4, and -2/3. Irrational numbers, on the other hand, cannot be expressed as such fractions. They are non-repeating, non-terminating decimals, like \sqrt{2} and \pi. From our example, since 12 is an integer, it can be expressed as \left( \frac{12}{1} \right). Therefore, 12 is a rational number.

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

In the following exercises, simplify. $$ \frac{1}{6} \cdot 17 \cdot 12 $$

In the following exercises, simplify the given expression. $$ -18\left(\frac{3}{2} n\right) $$

In the following exercises, simplify the given expression. $$ \left(\frac{8}{15}+\frac{2}{9}\right)+\frac{7}{9} $$

In the following exercises, evaluate each expression for the given value. If \(m=-13,\) evaluate: $$ (a)-\frac{2}{5}\left(\frac{5}{2} m\right) $$ $$ (b)\left(-\frac{2}{5} \cdot \frac{5}{2}\right) m $$

In the following exercises, simplify the given expression. $$ (12 a+4)-(9 a+6) $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.