Express in simplest radical form.start fraction, square root of, 28, end square root, divided by, 10, end fraction1028​ ​

1. Break Down the Problem

To express the fraction $\frac{\sqrt{28}}{10}$ in simplest radical form, we need to simplify $\sqrt{28}$ first.

2. Relevant Concepts

The square root can often be simplified by factoring out perfect squares. Here, we recognize that:

• $28 = 4 \times 7$
• Thus, $\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}$.

3. Analysis and Detail

Now, substituting back into the fraction, we have: $\frac{\sqrt{28}}{10} = \frac{2\sqrt{7}}{10}$ Next, we can simplify this fraction by dividing both the numerator and the denominator by 2: $\frac{2\sqrt{7}}{10} = \frac{\sqrt{7}}{5}$

4. Verify and Summarize

After simplification, we arrive at $\frac{\sqrt{7}}{5}$, which is indeed in simplest radical form since 7 is not a perfect square and cannot be simplified further.

Final Answer

$\frac{\sqrt{28}}{10} = \frac{\sqrt{7}}{5}$