To divide \( \sqrt{158} \) by \( \sqrt{12} \), you can use the property of square roots that states:
\[ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \]
Applying this property:
\[ \frac{\sqrt{158}}{\sqrt{12}} = \sqrt{\frac{158}{12}} \]
Now, simplify \( \frac{158}{12} \):
\[ \frac{158}{12} = \frac{79}{6} \]
This gives us:
\[ \sqrt{\frac{158}{12}} = \sqrt{\frac{79}{6}} = \frac{\sqrt{79}}{\sqrt{6}} \]
So, we can write the final answer as:
\[ \frac{\sqrt{79}}{\sqrt{6}} \]
If you want to further simplify \( \frac{\sqrt{79}}{\sqrt{6}} \), it can be rationalized:
\[ \frac{\sqrt{79}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}} = \frac{\sqrt{474}}{6} \]
Thus, \( \sqrt{158} \div \sqrt{12} \) can be expressed as:
\[ \frac{\sqrt{79}}{\sqrt{6}} \quad \text{or} \quad \frac{\sqrt{474}}{6} \]
However, the first form is already in a simplified form. Therefore, the final answer is:
\[ \frac{\sqrt{79}}{\sqrt{6}} \]
or
\[ \sqrt{\frac{79}{6}} \]
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