Explanation Given: The expression is 5 2 3 − 2 16 3 + 1 54 3 . Rules used: Rules for radical notation: 1. If a is a real number, n is positive integer, and a 1 / n is a real number then rational exponent expression a 1 / n is equivalent to radical expression a n . 2. If a is a real number, m is an integer, n is a positive integer, and a n is a real number, then radical notation of a m / n is either ( a n ) m or a m n . 3. If n is an even positive integer then, a n n = | a | and if n is an odd positive integer, then a n n = a . Rules for radicals For all real numbers a and b, and positive integers m and n for which the indicated roots are real numbers, then the following rules hold. a n ⋅ b n = a b n a b n = a n b n ( b ≠ 0 ) a n m = a m n Rules for simplified radicals: “An expression with radicals is simplified when the following conditions are satisfied. 1. The radicand has no factor raised to a power greater than or equal to the index. 2. The radicand has no fractions. 3. No denominator contains a radical(Rationalizing) 4. Exponents in the radicand and the index of the radical have no common factor. 5. All indicated operations have been performed if possible.” Calculation: The given expression is simplified as follows: 5 2 3 − 2 16 3 + 1 54 3 = 5 2 3 − 2 2 3 ⋅ 2 3 + 1 3 3 ⋅ 2 3 ( Rewrite radicals ) = 5 2 3 − 2 2 2 3 + 1 3 2 3 ( Factor out perfect

Pearson eText for Graphical Approach to College Algebra, A -- Instant Access (Pearson+)

7th Edition

ISBN: 9780137399918

Author: John Hornsby, Margaret Lial

Publisher: PEARSON+

See similar textbooks

Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Videos

Question

Chapter R.6, Problem 69E

To determine

The simplest form of 523−2163+1543.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter R.6, Problem 68E

Chapter R.6, Problem 70E

Students have asked these similar questions

Solve the following equation forx. leave answer in Simplified radical form. 5x²-4x-3=6

MATCHING LIST Question 6 Listen Use the given equations and their discriminants to match them to the type and number of solutions. 00 ed two irrational solutions a. x²+10x-2=-24 two rational solutions b. 8x²+11x-3=7 one rational solution c. 3x²+2x+7=2 two non-real solutions d. x²+12x+45 = 9 DELL FLOWER CHILD 10/20 All Changes S $681 22991

88 MULTIPLE CHOICE Question 7 Listen The following irrational expression is given in unsimplified form with four op- tions in simplified form. Select the correct simplified form. Select only one option. A 2±3√√2 B 4±√3 2±√ √3 D 1±√√3 DELL FLOWER CHILD 11/200 4 ± √48 4 ✓ All Changes Saved 165

Chapter R Solutions

Pearson eText for Graphical Approach to College Algebra, A -- Instant Access (Pearson+)

Ch. R.1 - Prob. 1E Ch. R.1 - Prob. 2E Ch. R.1 - Prob. 3E Ch. R.1 - Prob. 4E Ch. R.1 - Prob. 5E Ch. R.1 - Prob. 6E Ch. R.1 - Prob. 7E Ch. R.1 - Prob. 8E Ch. R.1 - Prob. 9E Ch. R.1 - Prob. 10E

Ch. R.1 - Prob. 11E Ch. R.1 - Prob. 12E Ch. R.1 - Prob. 13E Ch. R.1 - Prob. 14E Ch. R.1 - Prob. 15E Ch. R.1 - Prob. 16E Ch. R.1 - Prob. 17E Ch. R.1 - Prob. 18E Ch. R.1 - Prob. 19E Ch. R.1 - Prob. 20E Ch. R.1 - Prob. 21E Ch. R.1 - Prob. 22E Ch. R.1 - Prob. 23E Ch. R.1 - Prob. 24E Ch. R.1 - Prob. 25E Ch. R.1 - Prob. 26E Ch. R.1 - Prob. 27E Ch. R.1 - Prob. 28E Ch. R.1 - Prob. 29E Ch. R.1 - Prob. 30E Ch. R.1 - Prob. 31E Ch. R.1 - Prob. 32E Ch. R.1 - Prob. 33E Ch. R.1 - Prob. 34E Ch. R.1 - Prob. 35E Ch. R.1 - Prob. 36E Ch. R.1 - Prob. 37E Ch. R.1 - Prob. 38E Ch. R.1 - Prob. 39E Ch. R.1 - Prob. 40E Ch. R.1 - Prob. 41E Ch. R.1 - Prob. 42E Ch. R.1 - Prob. 43E Ch. R.1 - Prob. 44E Ch. R.1 - Prob. 45E Ch. R.1 - Prob. 46E Ch. R.1 - Prob. 47E Ch. R.1 - Prob. 48E Ch. R.1 - Prob. 49E Ch. R.1 - Prob. 50E Ch. R.1 - Prob. 51E Ch. R.1 - Prob. 52E Ch. R.1 - Prob. 53E Ch. R.1 - Prob. 54E Ch. R.1 - Prob. 55E Ch. R.1 - Prob. 56E Ch. R.1 - Prob. 57E Ch. R.1 - Prob. 58E Ch. R.1 - Prob. 59E Ch. R.1 - Let List the elements in each set B ∪ ∅ Ch. R.1 - Prob. 61E Ch. R.1 - Prob. 62E Ch. R.2 - Prob. 1E Ch. R.2 - Prob. 2E Ch. R.2 - Prob. 3E Ch. R.2 - Prob. 4E Ch. R.2 - Prob. 5E Ch. R.2 - Prob. 6E Ch. R.2 - Prob. 7E Ch. R.2 - Prob. 8E Ch. R.2 - Prob. 9E Ch. R.2 - Prob. 10E Ch. R.2 - Prob. 11E Ch. R.2 - Prob. 12E Ch. R.2 - Prob. 13E Ch. R.2 - Prob. 14E Ch. R.2 - Prob. 15E Ch. R.2 - Prob. 16E Ch. R.2 - Prob. 17E Ch. R.2 - Prob. 18E Ch. R.2 - Prob. 19E Ch. R.2 - Prob. 20E Ch. R.2 - Prob. 21E Ch. R.2 - Prob. 22E Ch. R.2 - Prob. 23E Ch. R.2 - Prob. 24E Ch. R.2 - Prob. 25E Ch. R.2 - Prob. 26E Ch. R.2 - Prob. 27E Ch. R.2 - Prob. 28E Ch. R.2 - Prob. 29E Ch. R.2 - Prob. 30E Ch. R.2 - Prob. 31E Ch. R.2 - Prob. 32E Ch. R.2 - Prob. 33E Ch. R.2 - Prob. 34E Ch. R.2 - Prob. 35E Ch. R.2 - Prob. 36E Ch. R.2 - Prob. 37E Ch. R.2 - Prob. 38E Ch. R.2 - Prob. 39E Ch. R.2 - Prob. 40E Ch. R.2 - Prob. 41E Ch. R.2 - Prob. 42E Ch. R.2 - Prob. 43E Ch. R.2 - Prob. 44E Ch. R.2 - Prob. 45E Ch. R.2 - Prob. 46E Ch. R.2 - Prob. 47E Ch. R.2 - Prob. 48E Ch. R.2 - Prob. 49E Ch. R.2 - Prob. 50E Ch. R.2 - Prob. 51E Ch. R.2 - Prob. 52E Ch. R.2 - Prob. 53E Ch. R.2 - Prob. 54E Ch. R.2 - Prob. 55E Ch. R.2 - Prob. 56E Ch. R.2 - Prob. 57E Ch. R.2 - Prob. 58E Ch. R.2 - Prob. 59E Ch. R.2 - Prob. 60E Ch. R.2 - Prob. 61E Ch. R.2 - Prob. 62E Ch. R.2 - Prob. 63E Ch. R.2 - Prob. 64E Ch. R.3 - Prob. 1E Ch. R.3 - Prob. 2E Ch. R.3 - Prob. 3E Ch. R.3 - Prob. 4E Ch. R.3 - Prob. 5E Ch. R.3 - Prob. 6E Ch. R.3 - Prob. 7E Ch. R.3 - Prob. 8E Ch. R.3 - Prob. 9E Ch. R.3 - Prob. 10E Ch. R.3 - Prob. 11E Ch. R.3 - Prob. 12E Ch. R.3 - Prob. 13E Ch. R.3 - Prob. 14E Ch. R.3 - Prob. 15E Ch. R.3 - Prob. 16E Ch. R.3 - Prob. 17E Ch. R.3 - Prob. 18E Ch. R.3 - Prob. 19E Ch. R.3 - Prob. 20E Ch. R.3 - Prob. 21E Ch. R.3 - Prob. 22E Ch. R.3 - Prob. 23E Ch. R.3 - Prob. 24E Ch. R.3 - Prob. 25E Ch. R.3 - Prob. 26E Ch. R.3 - Prob. 27E Ch. R.3 - Prob. 28E Ch. R.3 - Prob. 29E Ch. R.3 - Prob. 30E Ch. R.3 - Prob. 31E Ch. R.3 - Prob. 32E Ch. R.3 - Prob. 33E Ch. R.3 - Prob. 34E Ch. R.3 - Prob. 35E Ch. R.3 - Prob. 36E Ch. R.3 - Prob. 37E Ch. R.3 - Prob. 38E Ch. R.3 - Prob. 39E Ch. R.3 - Prob. 40E Ch. R.3 - Prob. 41E Ch. R.3 - Prob. 42E Ch. R.3 - Prob. 43E Ch. R.3 - Prob. 44E Ch. R.3 - Prob. 45E Ch. R.3 - Prob. 46E Ch. R.3 - Prob. 47E Ch. R.3 - Prob. 48E Ch. R.3 - Prob. 49E Ch. R.3 - Prob. 50E Ch. R.3 - Prob. 51E Ch. R.3 - Prob. 52E Ch. R.3 - Prob. 53E Ch. R.3 - Prob. 54E Ch. R.3 - Prob. 55E Ch. R.3 - Prob. 56E Ch. R.3 - Prob. 57E Ch. R.3 - Prob. 58E Ch. R.3 - Prob. 59E Ch. R.3 - Prob. 60E Ch. R.3 - Prob. 61E Ch. R.3 - Prob. 62E Ch. R.3 - Prob. 63E Ch. R.3 - Prob. 64E Ch. R.3 - Prob. 65E Ch. R.3 - Prob. 66E Ch. R.3 - Prob. 67E Ch. R.3 - Prob. 68E Ch. R.3 - Prob. 69E Ch. R.3 - Prob. 70E Ch. R.3 - Prob. 71E Ch. R.3 - Prob. 72E Ch. R.3 - Prob. 73E Ch. R.3 - Prob. 74E Ch. R.3 - Prob. 75E Ch. R.3 - Prob. 76E Ch. R.3 - Prob. 77E Ch. R.3 - Prob. 78E Ch. R.3 - Prob. 79E Ch. R.3 - Prob. 80E Ch. R.3 - Prob. 81E Ch. R.3 - Prob. 82E Ch. R.3 - Prob. 83E Ch. R.3 - Prob. 84E Ch. R.3 - Prob. 85E Ch. R.3 - Prob. 86E Ch. R.4 - Prob. 1E Ch. R.4 - Prob. 2E Ch. R.4 - Prob. 3E Ch. R.4 - Prob. 4E Ch. R.4 - Prob. 5E Ch. R.4 - Prob. 6E Ch. R.4 - Prob. 7E Ch. R.4 - Prob. 8E Ch. R.4 - Prob. 9E Ch. R.4 - Prob. 10E Ch. R.4 - Prob. 11E Ch. R.4 - Prob. 12E Ch. R.4 - Prob. 13E Ch. R.4 - Prob. 14E Ch. R.4 - Prob. 15E Ch. R.4 - Prob. 16E Ch. R.4 - Prob. 17E Ch. R.4 - Prob. 18E Ch. R.4 - Prob. 19E Ch. R.4 - Prob. 20E Ch. R.4 - Prob. 21E Ch. R.4 - Prob. 22E Ch. R.4 - Prob. 23E Ch. R.4 - Prob. 24E Ch. R.4 - Prob. 25E Ch. R.4 - Prob. 26E Ch. R.4 - Prob. 27E Ch. R.4 - Prob. 28E Ch. R.4 - Prob. 29E Ch. R.4 - Prob. 30E Ch. R.4 - Prob. 31E Ch. R.4 - Prob. 32E Ch. R.4 - Prob. 33E Ch. R.4 - Prob. 34E Ch. R.4 - Prob. 35E Ch. R.4 - Prob. 36E Ch. R.4 - Prob. 37E Ch. R.4 - Prob. 38E Ch. R.4 - Prob. 39E Ch. R.4 - Prob. 40E Ch. R.4 - Prob. 41E Ch. R.4 - Prob. 42E Ch. R.4 - Prob. 43E Ch. R.4 - Prob. 44E Ch. R.4 - Prob. 45E Ch. R.4 - Prob. 46E Ch. R.4 - Prob. 47E Ch. R.4 - Prob. 48E Ch. R.4 - Prob. 49E Ch. R.4 - Prob. 50E Ch. R.4 - Prob. 51E Ch. R.4 - Prob. 52E Ch. R.4 - Prob. 53E Ch. R.4 - Prob. 54E Ch. R.4 - Prob. 55E Ch. R.4 - Prob. 56E Ch. R.4 - Prob. 57E Ch. R.4 - Prob. 58E Ch. R.4 - Prob. 59E Ch. R.4 - Prob. 60E Ch. R.4 - Prob. 61E Ch. R.4 - Prob. 62E Ch. R.4 - Prob. 63E Ch. R.4 - Prob. 64E Ch. R.4 - Prob. 65E Ch. R.4 - Prob. 66E Ch. R.4 - Prob. 67E Ch. R.4 - Prob. 68E Ch. R.4 - Prob. 69E Ch. R.4 - Prob. 70E Ch. R.5 - Prob. 1E Ch. R.5 - Prob. 2E Ch. R.5 - Prob. 3E Ch. R.5 - Prob. 4E Ch. R.5 - Prob. 5E Ch. R.5 - Prob. 6E Ch. R.5 - Prob. 7E Ch. R.5 - Prob. 8E Ch. R.5 - Prob. 9E Ch. R.5 - Prob. 10E Ch. R.5 - Prob. 11E Ch. R.5 - Prob. 12E Ch. R.5 - Prob. 13E Ch. R.5 - Prob. 14E Ch. R.5 - Prob. 15E Ch. R.5 - Prob. 16E Ch. R.5 - Prob. 17E Ch. R.5 - Prob. 18E Ch. R.5 - Prob. 19E Ch. R.5 - Prob. 20E Ch. R.5 - Prob. 21E Ch. R.5 - Prob. 22E Ch. R.5 - Prob. 23E Ch. R.5 - Prob. 24E Ch. R.5 - Prob. 25E Ch. R.5 - Prob. 26E Ch. R.5 - Prob. 27E Ch. R.5 - Prob. 28E Ch. R.5 - Prob. 29E Ch. R.5 - Prob. 30E Ch. R.5 - Prob. 31E Ch. R.5 - Prob. 32E Ch. R.5 - Prob. 33E Ch. R.5 - Prob. 34E Ch. R.5 - Prob. 35E Ch. R.5 - Prob. 36E Ch. R.5 - Prob. 37E Ch. R.5 - Prob. 38E Ch. R.5 - Prob. 39E Ch. R.5 - Prob. 40E Ch. R.5 - Prob. 41E Ch. R.5 - Prob. 42E Ch. R.5 - Prob. 43E Ch. R.5 - Prob. 44E Ch. R.5 - Prob. 45E Ch. R.5 - Prob. 46E Ch. R.5 - Prob. 47E Ch. R.5 - Prob. 48E Ch. R.5 - Prob. 49E Ch. R.5 - Prob. 50E Ch. R.5 - Prob. 51E Ch. R.5 - Prob. 52E Ch. R.5 - Prob. 53E Ch. R.5 - Prob. 54E Ch. R.5 - Prob. 55E Ch. R.5 - Prob. 56E Ch. R.5 - Prob. 57E Ch. R.5 - Prob. 58E Ch. R.5 - Prob. 59E Ch. R.5 - Prob. 60E Ch. R.5 - Prob. 61E Ch. R.5 - Prob. 62E Ch. R.5 - Prob. 63E Ch. R.5 - Prob. 64E Ch. R.5 - Prob. 65E Ch. R.5 - Prob. 66E Ch. R.5 - Prob. 67E Ch. R.5 - Prob. 68E Ch. R.6 - Prob. 1E Ch. R.6 - Prob. 2E Ch. R.6 - Prob. 3E Ch. R.6 - Prob. 4E Ch. R.6 - Prob. 5E Ch. R.6 - Prob. 6E Ch. R.6 - Prob. 7E Ch. R.6 - Prob. 8E Ch. R.6 - Prob. 9E Ch. R.6 - Prob. 10E Ch. R.6 - Prob. 11E Ch. R.6 - Prob. 12E Ch. R.6 - Prob. 13E Ch. R.6 - Prob. 14E Ch. R.6 - Prob. 15E Ch. R.6 - Prob. 16E Ch. R.6 - Prob. 17E Ch. R.6 - Prob. 18E Ch. R.6 - Prob. 19E Ch. R.6 - Prob. 20E Ch. R.6 - Prob. 21E Ch. R.6 - Prob. 22E Ch. R.6 - Prob. 23E Ch. R.6 - Prob. 24E Ch. R.6 - Prob. 25E Ch. R.6 - Prob. 26E Ch. R.6 - Prob. 27E Ch. R.6 - Prob. 28E Ch. R.6 - Prob. 29E Ch. R.6 - Prob. 30E Ch. R.6 - Prob. 31E Ch. R.6 - Prob. 32E Ch. R.6 - Prob. 33E Ch. R.6 - Prob. 34E Ch. R.6 - Prob. 35E Ch. R.6 - Prob. 36E Ch. R.6 - Prob. 37E Ch. R.6 - Prob. 38E Ch. R.6 - Prob. 39E Ch. R.6 - Prob. 40E Ch. R.6 - Prob. 41E Ch. R.6 - Prob. 42E Ch. R.6 - Prob. 43E Ch. R.6 - Prob. 44E Ch. R.6 - Prob. 45E Ch. R.6 - Prob. 46E Ch. R.6 - Prob. 47E Ch. R.6 - Prob. 48E Ch. R.6 - Prob. 49E Ch. R.6 - Prob. 50E Ch. R.6 - Prob. 51E Ch. R.6 - Prob. 52E Ch. R.6 - Prob. 53E Ch. R.6 - Prob. 54E Ch. R.6 - Prob. 55E Ch. R.6 - Prob. 56E Ch. R.6 - Prob. 57E Ch. R.6 - Prob. 58E Ch. R.6 - Prob. 59E Ch. R.6 - Prob. 60E Ch. R.6 - Prob. 61E Ch. R.6 - Prob. 62E Ch. R.6 - Prob. 63E Ch. R.6 - Prob. 64E Ch. R.6 - Prob. 65E Ch. R.6 - Prob. 66E Ch. R.6 - Prob. 67E Ch. R.6 - Prob. 68E Ch. R.6 - Prob. 69E Ch. R.6 - Prob. 70E Ch. R.6 - Prob. 71E Ch. R.6 - Prob. 72E Ch. R.6 - Prob. 73E Ch. R.6 - Prob. 74E Ch. R.6 - Prob. 75E Ch. R.6 - Prob. 76E Ch. R.6 - Prob. 77E Ch. R.6 - Prob. 78E Ch. R.6 - Prob. 79E Ch. R.6 - Prob. 80E Ch. R.6 - Prob. 81E Ch. R.6 - Prob. 82E Ch. R.6 - Prob. 83E Ch. R.6 - Rationalize the denominator of each radical...Ch. R.6 - Prob. 85E Ch. R.6 - Prob. 86E Ch. R.6 - Prob. 87E Ch. R.6 - Prob. 88E Ch. R.6 - Prob. 89E Ch. R.6 - Prob. 90E Ch. R - Prob. 1T Ch. R - Prob. 2T Ch. R - Prob. 3T Ch. R - Prob. 4T Ch. R - Prob. 5T Ch. R - Prob. 6T Ch. R - Prob. 7T Ch. R - Prob. 8T Ch. R - Prob. 9T Ch. R - Prob. 10T Ch. R - Prob. 11T Ch. R - Prob. 12T Ch. R - Prob. 13T Ch. R - Prob. 14T Ch. R - Prob. 15T Ch. R - Prob. 16T Ch. R - Prob. 17T Ch. R - Prob. 18T Ch. R - Prob. 19T Ch. R - Prob. 20T Ch. R - Prob. 21T Ch. R - Prob. 22T Ch. R - Prob. 23T Ch. R - Prob. 24T Ch. R - Prob. 25T Ch. R - Prob. 26T Ch. R - Prob. 27T Ch. R - Prob. 28T Ch. R - Prob. 29T Ch. R - Prob. 30T Ch. R - Prob. 31T Ch. R - Prob. 32T Ch. R - Prob. 33T Ch. R - Prob. 34T Ch. R - Prob. 35T Ch. R - Prob. 36T Ch. R - Prob. 37T Ch. R - Prob. 38T Ch. R - Prob. 39T Ch. R - Prob. 40T Ch. R - Prob. 41T Ch. R - Prob. 42T Ch. R - Prob. 43T Ch. R - Prob. 44T Ch. R - Prob. 45T Ch. R - Prob. 46T

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The simplest form of 5 2 3 − 2 16 3 + 1 54 3 .

Concept explainers

Videos

The simplest form of 523−2163+1543.

Want to see the full answer?

Chapter R Solutions