/*! 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 36 Find each root. $$ \sqrt{\fr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 36

Find each root. $$ \sqrt{\frac{100}{9}} $$

Short Answer

Expert verified
\(\frac{10}{3}\)

Step by step solution

01

- Simplify the fraction under the square root

The given expression is \(\frac{100}{9}\). Simplify the fraction by calculating the square root of the numerator and the square root of the denominator separately.
02

- Find the square root of the numerator

The numerator is 100. The square root of 100 is 10, because \(10^2 = 100\).
03

- Find the square root of the denominator

The denominator is 9. The square root of 9 is 3, because \(3^2 = 9\).
04

- Combine the results

Combine the results from Step 2 and Step 3. Thus, the square root of \(\frac{100}{9}\) is \(\frac{10}{3}\).

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 represents a number that, when multiplied by itself, equals the original number. For example, the square root of 100 is 10 because 10 multiplied by 10 equals 100. In mathematical notation, this is written as \(\backslash sqrt{100} = 10\). Similarly, the square root of 9 is 3 because 3 multiplied by 3 equals 9, written as \(\backslash sqrt{9} = 3\). Understanding square roots is crucial for solving problems that involve radical expressions, such as the one in the given exercise. Remember, when dealing with square roots, always ensure to find the positive root as it is typically what's referred to in most contexts.
numerator and denominator
In a fraction, the numerator is the top number, and the denominator is the bottom number. The fraction as a whole represents the division of the numerator by the denominator. For example, in \( \frac{100}{9} \), 100 is the numerator and 9 is the denominator. It's important to understand this because, when simplifying square roots within fractions, you will need to handle the numerator and denominator separately. Ensuring that you correctly identify these parts will help simplify complex fractions effectively and prevent any mistakes.
simplifying fractions
Simplifying fractions involves reducing the fraction to its simplest form. For a fraction under a square root, like \( \frac{\backslash sqrt{a}}{\backslash sqrt{b}} \), you simplify by taking the square root of the numerator and the denominator independently. To solve \( \frac{\backslash sqrt{100}}{\backslash sqrt{9}} \), you find the square root of 100, which is 10, and the square root of 9, which is 3. This results in \( \frac{10}{3} \). This process is essential in algebra to make expressions easier to handle and solve. Remember, after simplifying, always check if the fraction can be reduced further.

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

Simplify each expression. Assume that all variables represent positive real numbers. $$ -8 y^{11 / 7}\left(y^{3 / 7}-y^{-4 / 7}\right) $$

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{3 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}} $$

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{-1}{3 \sqrt{2}-2 \sqrt{7}} $$

Graph each circle. Identify the center and the radius. \((x-2)^{2}+(y-3)^{2}=4\)

Rationalize each denominator. Assume that all variables represent positive real numbers. $$ \frac{5 \sqrt{2 m}}{\sqrt{y^{3}}} $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.