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Write radical form. -54 in simplest

Write radical form. -54 in simplest

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Simplifying Radicals with Negative
**Question:** Write \(\sqrt{-54}\) in simplest radical form. **Explanation:** To express \(\sqrt{-54}\) in simplest radical form, we need to break it down into its components: 1. Recognize that \(\sqrt{-54}\) involves the square root of a negative number. This can be rewritten using the imaginary unit \(i\), where \(i = \sqrt{-1}\). 2. Rewrite the expression as \(\sqrt{-1} \times \sqrt{54} = i\sqrt{54}\). 3. Simplify \(\sqrt{54}\). The number 54 can be factored into \(54 = 2 \times 3^3\). 4. Extract the square root of the perfect square from this factorization: \(\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}\). 5. Combine with the imaginary unit: \(i\sqrt{54} = i(3\sqrt{6}) = 3i\sqrt{6}\). Thus, the simplest radical form of \(\sqrt{-54}\) is \(3i\sqrt{6}\).
Transcribed Image Text:**Question:** Write \(\sqrt{-54}\) in simplest radical form. **Explanation:** To express \(\sqrt{-54}\) in simplest radical form, we need to break it down into its components: 1. Recognize that \(\sqrt{-54}\) involves the square root of a negative number. This can be rewritten using the imaginary unit \(i\), where \(i = \sqrt{-1}\). 2. Rewrite the expression as \(\sqrt{-1} \times \sqrt{54} = i\sqrt{54}\). 3. Simplify \(\sqrt{54}\). The number 54 can be factored into \(54 = 2 \times 3^3\). 4. Extract the square root of the perfect square from this factorization: \(\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}\). 5. Combine with the imaginary unit: \(i\sqrt{54} = i(3\sqrt{6}) = 3i\sqrt{6}\). Thus, the simplest radical form of \(\sqrt{-54}\) is \(3i\sqrt{6}\).
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