Question

Express in simplest radical form.
start fraction, square root of, 12, end square root, divided by, square root of, 2, end square root, end fraction
2
​

12
​

​

Answer
Attempt 1 out of 5

Answer 1

To simplify the expression \(\frac{\sqrt{12}}{\sqrt{2}}\), you can use the property of radicals that states \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\).

So, we can rewrite the expression as:

\[
\frac{\sqrt{12}}{\sqrt{2}} = \sqrt{\frac{12}{2}} = \sqrt{6}
\]

Next, we simplify \(\sqrt{12}\) first, if needed:

\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]

Now, substituting back into the expression:

\[
\frac{\sqrt{12}}{\sqrt{2}} = \frac{2\sqrt{3}}{\sqrt{2}} = 2\cdot\frac{\sqrt{3}}{\sqrt{2}} = 2\sqrt{\frac{3}{2}}
\]

But we'll use the first simplification for the simplest radical form which is:

\[
\sqrt{6}
\]

So, the final simplified answer is:

\[
\sqrt{6}
\]