Question

Simplify the expression. $\sqrt[4]{48}-\sqrt[4]{3}$

   Simplify the expression.
$\sqrt[4]{48}-\sqrt[4]{3}$

Algebra and Trigonometry

Algebra and Trigonometry

James Stewart,… 2nd Edition

Chapter 0, Problem 32

Instant Answer

Solved by Expert Amy Jiang

08/27/2020

Step 1

So, $\sqrt[4]{48}$ becomes $\sqrt[4]{16 \times 3}$. Show more…

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Simplify the expression. $\sqrt[4]{48}-\sqrt[4]{3}$

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Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, or fourth roots, that represent the inverse operation of raising a number to a certain power. Understanding radicals is fundamental, as the process of simplification often involves rewriting a radical expression by extracting factors that are perfect powers matching the index of the radical.

nth Roots and Rational Exponents

The concept of nth roots, where the nth root of a number is the same as raising that number to the power of 1/n, allows for easier manipulation of expressions using the laws of exponents. This is particularly useful in transforming radical expressions into forms that are easier to simplify or combine.

Exponent Rules

Exponent rules, including laws for multiplying and dividing powers with the same base and converting between radical and exponent notation, are critical for simplifying expressions that involve roots. These rules provide a systematic way to manipulate and reduce expressions by handling exponents effectively.

Factoring Techniques

Factoring involves breaking down expressions into a product of simpler factors, and it is an important technique in simplification of radical expressions. By identifying and extracting common factors or perfect power components from the radicand, one can separate the expression into parts that simplify individually, leading to a more concise overall expression.

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