Question

Solve each equation. $$ 2+4 z^{\frac{1}{2}}=0 $$

   Solve each equation. 
$$
2+4 z^{\frac{1}{2}}=0
$$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 7, Problem 14

Instant Answer

Solved by Expert Carolyn Crouch

03/11/2020

Step 1

Step 1: Subtract 2 from both sides of the equation to isolate the term with the variable: $$ 4 z^{\frac{1}{2}}=-2 $$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve each equation. $$ 2+4 z^{\frac{1}{2}}=0 $$

Play audio

Feedback

Powered by NumerAI

Carolyn Crouch and 80 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

Domain Considerations

When dealing with radicals, it is important to consider the domain of the function. For example, the square root function is generally defined to return non-negative values in the realm of real numbers, which can affect the existence of real solutions and might lead one to extend the discussion to complex numbers if necessary.

Extraneous Solutions

Extraneous solutions are potential answers that emerge from algebraic manipulations—such as squaring both sides of an equation—that may not satisfy the original equation. Recognizing and verifying solutions is crucial to ensure that only valid solutions are accepted.

Radical Equations

Radical equations are equations in which the unknown variable appears under a radical sign. Solving these equations typically involves isolating the radical expression and then raising both sides of the equation to a power that eliminates the radical, keeping in mind the need to check for any solutions that might not satisfy the original equation.

Fractional Exponents

Fractional exponents represent radical operations; for example, an exponent of 1/2 indicates taking the square root. Understanding this connection allows one to convert between radical and exponent notation, which is essential for manipulating and solving equations that involve roots.

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