Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

Previous problemNext problem

1:31 minutes

Problem 53

Textbook Question

Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜ m² • ∜ m²

Verified step by step guidance

Recognize that the expression involves multiplying two fourth roots: \( \sqrt[4]{m^2} \cdot \sqrt[4]{m^2} \).

Use the property of radicals that states \( \sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b} \).

Apply this property to combine the radicals: \( \sqrt[4]{m^2} \cdot \sqrt[4]{m^2} = \sqrt[4]{m^2 \cdot m^2} \).

Simplify the expression inside the radical: \( m^2 \cdot m^2 = m^4 \).

Now, simplify the radical: \( \sqrt[4]{m^4} \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radical Expressions

Radical expressions involve roots, such as square roots or fourth roots, and are represented using the radical symbol (√). In this context, ∜m² denotes the fourth root of m squared. Understanding how to manipulate these expressions is crucial for performing operations like multiplication and simplification.

Properties of Exponents

The properties of exponents govern how to handle expressions involving powers. For instance, when multiplying like bases, you add the exponents. In the case of radicals, the expression ∜m² can be rewritten using fractional exponents, specifically m^(2/4) or m^(1/2), which aids in simplifying the operation.

Multiplication of Radicals

When multiplying radical expressions, the product of the radicands (the numbers or expressions inside the radical) can be taken under a single radical. For example, ∜m² • ∜m² can be combined as ∜(m² • m²), which simplifies to ∜(m^4). This principle is essential for simplifying the expression correctly.