Question

Solve each equation. $$\sqrt[4]{x-15}=2$$

   Solve each equation.
$$\sqrt[4]{x-15}=2$$

Precalculus Student Solutions Manual 5th

Precalculus Student Solutions Manual 5th

Margaret L. Lial,… 5th Edition

Chapter 1, Problem 61

Instant Answer

Solved by Expert Dale Sanford

08/06/2020

Step 1

This gives us: $$(\sqrt[4]{x-15})^4 = 2^4$$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve each equation. $$\sqrt[4]{x-15}=2$$

Play audio

Feedback

Powered by NumerAI

Dale Sanford and 68 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Properties of Radicals and Exponents

Understanding the relationship between radicals and exponents is crucial. A radical expression can be rewritten as an expression with a fractional exponent, and applying an exponent that corresponds to the radical index can eliminate the radical. This concept allows for the transformation of a radical equation into a polynomial equation, which can then be solved using standard algebraic techniques.

Inverse Operations in Equation Solving

Inverse operations are used to 'undo' a mathematical operation in order to isolate the variable. In the context of radical equations, raising both sides of the equation to a power that is the reciprocal of the root enables the removal of the radical sign, effectively converting the equation into a simpler form that can be solved more directly.

Radical Equations

These are equations that include a radical expression where the variable appears under a radical sign. Solving radical equations often requires isolating the radical, applying appropriate inverse operations, and checking for extraneous solutions, as the process of raising both sides to a power may introduce solutions that do not satisfy the original equation.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later