Question

Divide. √158÷√12 Enter your answer in the boxes in simplified form.

Answer 1

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

\[
\sqrt{\frac{79}{6}}
\]