To simplify the expression \(\sqrt{\frac{28h^4}{25}}\), we can break it down as follows:
- Start by separating the square root of the numerator and the square root of the denominator:
\[ \sqrt{\frac{28h^4}{25}} = \frac{\sqrt{28h^4}}{\sqrt{25}} \]
- We know that \(\sqrt{25} = 5\), so we simplify the denominator:
\[ \frac{\sqrt{28h^4}}{5} \]
- Next, we simplify the expression in the numerator. We can separate the square root of \(28\) and \(h^4\):
\[ \sqrt{28h^4} = \sqrt{28} \cdot \sqrt{h^4} \]
- Calculate \(\sqrt{h^4}\):
\[ \sqrt{h^4} = h^2 \quad \text{(since \(h > 0\))} \]
- Now, we need to simplify \(\sqrt{28}\). We can express \(28\) as \(4 \cdot 7\):
\[ \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \]
- Putting it all together, we have:
\[ \sqrt{28h^4} = 2\sqrt{7} \cdot h^2 \]
- Substitute this back into the expression:
\[ \frac{\sqrt{28h^4}}{5} = \frac{2h^2\sqrt{7}}{5} \]
Thus, the simplified form of \(\sqrt{\frac{28h^4}{25}}\) is:
\[ \frac{2h^2\sqrt{7}}{5} \]
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