Question

Express in simplest radical form.
start fraction, square root of, 252, end square root, divided by, 2, end fraction
2
252
​

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Answer
Attempt 1 out of 5

Submit Answer
square root of, end square root
x
​

Answer 1

To express \(\frac{\sqrt{252}}{2}\) in simplest radical form, we start by simplifying \(\sqrt{252}\).

The number 252 can be factored into its prime factors:
\[
252 = 2^2 \times 3^2 \times 7
\]

Now we take the square root:
\[
\sqrt{252} = \sqrt{2^2 \times 3^2 \times 7} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{7}
\]
\[
= 2 \times 3 \times \sqrt{7} = 6\sqrt{7}
\]

Now, we can substitute this back into the original expression:
\[
\frac{\sqrt{252}}{2} = \frac{6\sqrt{7}}{2}
\]

Now we simplify this:
\[
\frac{6\sqrt{7}}{2} = 3\sqrt{7}
\]

Thus, the answer in simplest radical form is:
\[
\boxed{3\sqrt{7}}
\]