Dharmendra Jain

verified

This problem has been solved

by verified expert Dharmendra Jain

100% free to try

Question

Write in terms of $i$ and then simplify. $$\sqrt{-16} \cdot \sqrt{-4}$$

   Write in terms of $i$ and then simplify.
$$\sqrt{-16} \cdot \sqrt{-4}$$

Trigonometry

Charles P. McKeague,… 7th Edition

Chapter 8, Problem 26

Instant Answer

Solved by Expert Dharmendra Jain

10/30/2020

Step 1

Step 1: We can rewrite the given expression as follows: $$\sqrt{-16} \cdot \sqrt{-4} = \sqrt{16} \cdot \sqrt{-1} \cdot \sqrt{4} \cdot \sqrt{-1}$$ Show more…

Show all steps

lock

Thanks for your feedback!

Write in terms of $i$ and then simplify. $$\sqrt{-16} \cdot \sqrt{-4}$$

Play audio

Feedback

Powered by NumerAI

Dharmendra Jain and 60 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 Radical Expressions

Radical expressions obey specific algebraic rules, including the product rule, which states that ?(ab) = ?(a)?(b). However, when dealing with negative radicands, it is important to apply these rules carefully within the context of complex numbers using the imaginary unit.

Square Roots of Negative Numbers

The square root of a negative number is expressed by factoring out -1 and applying the imaginary unit, such that ?(-a) is rewritten as i?(a). This conversion is essential for simplifying expressions that involve the square roots of negative quantities.

Imaginary Unit (i)

The imaginary unit, denoted as i, is defined by the property i² = -1. This definition allows us to express the square roots of negative numbers in terms of i, effectively extending the domain of the square root function to include certain non-real numbers.

Complex Numbers

Complex numbers extend the real number system by including numbers of the form a + bi, where a is the real component and b is the imaginary component. They provide a framework to handle operations that do not have real solutions, such as the square roots of negative numbers.

Recommended Videos

Transcript

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

Start Using Ace