Question

Rationalize the denominator. $$\frac{-2}{\sqrt[5]{y}}$$

   Rationalize the denominator.
$$\frac{-2}{\sqrt[5]{y}}$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 10, Problem 44

Instant Answer

Solved by Expert Prashansha Kaushik

03/29/2021

Step 1

This gives us: $$\frac{-2 \cdot \sqrt[5]{y^{4}}}{\sqrt[5]{y} \cdot \sqrt[5]{y^{4}}}$$ Show more…

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Rationalize the denominator. $$\frac{-2}{\sqrt[5]{y}}$$

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Key Concepts

Rationalizing the Denominator

This concept involves rewriting an expression so that the denominator does not contain any irrational numbers or radicals. It is a common practice in algebra to simplify expressions and make further operations more straightforward.

Radicals and Nth Roots

Radicals represent roots of numbers, such as square roots, cube roots, or in general, nth roots. Understanding radicals in terms of fractional exponents (for example, the nth root of a number can be written as the number raised to the power of 1/n) facilitates their manipulation and simplification in algebraic expressions.

Multiplicative Identity and Appropriate Multiplication Factors

To rationalize a denominator that contains a radical, you multiply both the numerator and the denominator by an appropriate factor. This factor, which is essentially 1 in a disguised form, is chosen so that when it multiplies the radical in the denominator, the radical is eliminated or its index is resolved, resulting in a rational number.

Exponent Rules

Understanding and applying the laws of exponents is essential when dealing with radicals expressed as fractional exponents. This includes rules such as when multiplying powers with the same base, the exponents are added. These rules help in determining the correct factor needed to eliminate the radical in the denominator.

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