/*! 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 100 Simplify. 532--\sqrt{5}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 100

Simplify. 532--\sqrt{5}

Short Answer

Expert verified
The expression 532 - \(\sqrt{5}\) is already simplified.

Step by step solution

01

Understand the Expression

The given expression is 532 - \(\sqrt{5}\). It involves a whole number, 532, and the square root of 5, which is an irrational number.
02

Identify Simplification Requirement

In this case, the expression already appears in a simplified form: a whole number minus a square root value. There are no like terms or further simplifications possible within the expression itself.
03

Interpretation of the Expression

When asked to simplify an expression like 532 - \(\sqrt{5}\), it means presenting it in a manner that combines like terms or reduces in any possible way, which, in this case, isn't applicable. Hence, the expression is as simplified as possible.

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 Whole Numbers
Whole numbers are the set of numbers that include zero and all the positive integers without any fractions or decimals. In other words, numbers like 0, 1, 2, 3, and so on are whole numbers. They are practical and used in everyday counting and calculations.
Whole numbers have the following characteristics:
  • They do not include negative numbers or fractions.
  • They begin at zero and increase by increments of one.
  • All whole numbers are also integers, but not all integers are whole numbers since integers include negative numbers too.
In the exercise example, 532 is a whole number. It is simple and complete, making it easy to handle in mathematical expressions.
Exploring Irrational Numbers
Irrational numbers are numbers that cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions. A famous example of an irrational number is \( \pi \).
These numbers are crucial in mathematics, as they provide many real-life solutions.
  • An irrational number like \( \sqrt{5} \) has a decimal form that doesn鈥檛 end or repeat.
  • They often involve roots, such as square roots, that cannot be simplified into neat fractions or whole numbers.
In the expression 532 - \( \sqrt{5} \), \( \sqrt{5} \) represents the irrational part, resisting simplification into a fraction or decimal number that makes clean calculations easy.
Recognizing Like Terms
Like terms in algebra are terms that have the same variables raised to the same power. They can be combined to simplify expressions. For example, in the term \(3x + 4x\), both terms are like because they contain the variable \(x\) raised to the same power, so they can be combined to make \(7x\).
However, not all expressions contain like terms.
  • Like terms must have identical variables and exponents but can have different coefficients.
  • Whole numbers without variables are considered like terms.
In the expression 532 - \( \sqrt{5} \), there are no like terms because 532 is a whole number and \( \sqrt{5} \) is an irrational term. Thus, no further simplification or combination is possible, and the expression stands as it is.

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. (Assume all radicands containing variable expressions are positive.) \(16 y 2---\sqrt{4}+81 y 2----\sqrt{4}\)

Simplify. (Assume all radicands containing variable expressions are positive.) \(49 x---\sqrt{-9} y--\sqrt{+} x \sqrt{-4} y--\sqrt{1}\)

Simplify. (Assume all radicands containing variable expressions are positive.) \(a \cdot 3 b--\sqrt{5}+4 a \cdot 3 b--\sqrt{5}-a \cdot 3 b-\sqrt{5}\)

Use the distance formula to calculate the distance between the given two points. $$ (-5,-2) \text { and }(1,-6) $$

Rationalize the denominator $$ 236-\sqrt{3} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete 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.