1. **State the problem:** Simplify the expression $$\sqrt{3^{\frac{6}{25}}}$$. 2. **Recall the rule:** The square root of a number is the same as raising that number to the power of $\frac{1}{2}$. So, $$\sqrt{a} = a^{\frac{1}{2}}$$. 3. **Apply the rule:** Rewrite the expression as $$\left(3^{\frac{6}{25}}\right)^{\frac{1}{2}}$$. 4. **Use the power of a power rule:** When raising a power to another power, multiply the exponents: $$\left(a^{m}\right)^{n} = a^{m \times n}$$. 5. **Calculate the new exponent:** $$\frac{6}{25} \times \frac{1}{2} = \frac{6}{50} = \frac{3}{25}$$. 6. **Write the simplified expression:** $$3^{\frac{3}{25}}$$. **Final answer:** $$\sqrt{3^{\frac{6}{25}}} = 3^{\frac{3}{25}}$$.