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To express \(\sqrt{5^{\frac{5}{4}}}\) in its simplest radical form, let's break down the problem step-by-step.

1. Start with the expression:  
   \[
   \sqrt{5^{\frac{5}{4}}}
   \]

2. Rewrite the square root as an exponent of \(\frac{1}{2}\):
   \[
   (5^{\frac{5}{4}})^{\frac{1}{2}}
   \]

3. Multiply the exponents \(\frac{5}{4} \times \frac{1}{2} = \frac{5}{8}\):
   \[
   5^{\frac{5}{8}}
   \]

So, the simplest radical form of \(\sqrt{5^{\frac{5}{4}}}\) is:
\[
5^{\frac{5}{8}}
\]

Would you like a deeper explanation of any steps?

Here are some related questions that might interest you:
1. How do you simplify expressions with fractional exponents?
2. What is the general rule for simplifying expressions under a square root?
3. How can we rewrite radical expressions as fractional exponents?
4. How do fractional exponents relate to roots?
5. How do you handle expressions with exponents raised to other exponents?

**Tip:** When simplifying expressions with roots and exponents, converting them to fractional exponents can often make the process more straightforward.

State in the simplest radical form \(\sqrt{5^{\frac{5}{4}}}\)

Learn how to simplify \(\sqrt{5^{\frac{5}{4}}}\) to its simplest radical form using properties of exponents. This problem covers key concepts in radicals and fractional exponents, ideal for high school students studying advanced algebra topics.

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