Question

What is the value of each expression? $\sqrt[5]{1}$

   What is the value of each expression?
$\sqrt[5]{1}$

Algebra 1 Common Core

Algebra 1 Common Core

Randall I.… 1st Edition

Chapter 7, Problem 12

Instant Answer

Solved by Expert Zach Steedman

04/01/2020

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This means we need to find a number that, when multiplied by itself 5 times, equals 1. Show more…

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What is the value of each expression? $\sqrt[5]{1}$

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Key Concepts

Radical Notation

Radical notation is a way of expressing roots of numbers, where the radical symbol (?) denotes the extraction of a number that, when raised to a given power, equals the original number. This notation is not limited to square roots; it extends to cube roots, fourth roots, and in general, nth roots, making it a fundamental concept in algebra and higher mathematics.

nth Root

The nth root of a number is defined as the number that, when raised to the power of n, produces the original number. This concept generalizes the idea of square roots to any exponent and is essential for solving equations involving exponents, simplifying expressions, and understanding the behavior of functions in both real and complex contexts.

Properties of Unity

The number 1 has unique properties in arithmetic and algebra. One important property is that any positive integer power of 1 is 1. This property extends to the concept of roots, so that the nth root of 1 is 1 in the real number system. Understanding these properties is crucial as they often simplify the evaluation of algebraic expressions and serve as a basis for more complex discussions of numbers, such as the study of the nth roots of unity in complex analysis.

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