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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]
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