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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]

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