The mathematical expression in the image is: \[ (\sqrt{-4x})(\sqrt{-5x}) \] This expression involves the multiplication of two square roots. Each square root contains a negative number multiplied by the variable \(x\). To simplify this expression, you can apply the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). Therefore, multiplying inside the square roots gives: \[ \sqrt{(-4x) \cdot (-5x)} = \sqrt{20x^2} \] This can be further simplified to: \[ \sqrt{20} \cdot x \] Finally, \(\sqrt{20}\) can be expressed as \(2\sqrt{5}\), so the fully simplified form is: \[ 2x\sqrt{5} \]

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please simplify The following operation.
The mathematical expression in the image is:

\[
(\sqrt{-4x})(\sqrt{-5x})
\]

This expression involves the multiplication of two square roots. Each square root contains a negative number multiplied by the variable \(x\). 

To simplify this expression, you can apply the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). Therefore, multiplying inside the square roots gives:

\[
\sqrt{(-4x) \cdot (-5x)} = \sqrt{20x^2}
\]

This can be further simplified to:

\[
\sqrt{20} \cdot x
\]

Finally, \(\sqrt{20}\) can be expressed as \(2\sqrt{5}\), so the fully simplified form is:

\[
2x\sqrt{5}
\]
Transcribed Image Text:The mathematical expression in the image is: \[ (\sqrt{-4x})(\sqrt{-5x}) \] This expression involves the multiplication of two square roots. Each square root contains a negative number multiplied by the variable \(x\). To simplify this expression, you can apply the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). Therefore, multiplying inside the square roots gives: \[ \sqrt{(-4x) \cdot (-5x)} = \sqrt{20x^2} \] This can be further simplified to: \[ \sqrt{20} \cdot x \] Finally, \(\sqrt{20}\) can be expressed as \(2\sqrt{5}\), so the fully simplified form is: \[ 2x\sqrt{5} \]
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