Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

reduce the square root of -8

Sagot :

We have to simplify:

[tex]\sqrt[]{-8}[/tex]

We first use the radical property shown below to write it as:

Radical Property:

[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}[/tex]

Thus, we can write this problem as:

[tex]\sqrt[]{-8}=\sqrt[]{(-1)(8)}=\sqrt[]{-1}\sqrt[]{8}[/tex]

We know the square root of -1 is i, thus we may write:

[tex]\sqrt[]{8}i[/tex]

Now we can again use the radical property to break apart root 8. Shown below:

[tex]\begin{gathered} \sqrt[]{8}i \\ =\sqrt[]{2\times2\times2}i \\ =\sqrt[]{2}\sqrt[]{2}\sqrt[]{2}i \end{gathered}[/tex]

Now we can further simply using

[tex]\sqrt[]{x}\sqrt[]{x}=x[/tex]

Thus, the final simplification would be:

[tex]\sqrt[]{-8=}2\sqrt[]{2}i[/tex]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.