Question

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state. x$\sqrt[3]{-\frac{216}{1331}}$

Name: Problem 28, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2021-06-14T21:31:22-08:00
Duration: 1 min
Channel: Julie Silva
Description: Evaluate each radical expression if it is a real number. If the expression is not a real number, so state. x√(-(216)/(1331))

   Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
x$\sqrt[3]{-\frac{216}{1331}}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 28

Instant Answer

Solved by Expert Julie Silva

06/14/2021

Step 1

First, we can simplify the expression inside the cube root: $-\frac{216}{1331} = -\frac{6^3}{11^3}$ Now, we can take the cube root of each part: $\sqrt[3]{-\frac{6^3}{11^3}} = \frac{\sqrt[3]{6^3}}{\sqrt[3]{11^3}} = \frac{6}{11}$ Show more…

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Evaluate each radical expression if it is a real number. If the expression is not a real number, so state. x$\sqrt[3]{-\frac{216}{1331}}$

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Key Concepts

Cube Roots

Cube roots refer to the operation of finding a number that, when multiplied by itself three times, equals the original number. Unlike square roots, cube roots are defined for negative numbers because multiplying three negative factors results in a negative product.

Radical Expression Simplification

Simplifying radical expressions involves identifying factors within the radicand that are perfect powers corresponding to the radical's degree. For cube roots, both the numerator and the denominator can be broken down into perfect cubes, which can then be individually extracted to simplify the expression.

Rational Numbers

When working with radicals that involve fractions, if the numerator and denominator are perfect cubes, they can be separately simplified. This process converts the radical expression into a simpler form expressed as a rational number, making it more straightforward to work with in further calculations.

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