1. **State the problem:** Solve the equation $$\sqrt{x} \times \sqrt{x} \times \sqrt{x} = 6$$. 2. **Rewrite the expression:** Recall that $$\sqrt{x} = x^{\frac{1}{2}}$$. So the left side becomes: $$\sqrt{x} \times \sqrt{x} \times \sqrt{x} = x^{\frac{1}{2}} \times x^{\frac{1}{2}} \times x^{\frac{1}{2}}$$. 3. **Use the rule of exponents:** When multiplying powers with the same base, add the exponents: $$x^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}} = x^{\frac{3}{2}}$$. 4. **Rewrite the equation:** $$x^{\frac{3}{2}} = 6$$. 5. **Solve for x:** To isolate $$x$$, raise both sides to the power of the reciprocal of $$\frac{3}{2}$$, which is $$\frac{2}{3}$$: $$\left(x^{\frac{3}{2}}\right)^{\frac{2}{3}} = 6^{\frac{2}{3}}$$. 6. **Simplify the left side:** $$x^{\cancel{\frac{3}{2}} \times \cancel{\frac{2}{3}}} = x^1 = x$$. 7. **Simplify the right side:** $$6^{\frac{2}{3}} = \left(6^{\frac{1}{3}}\right)^2 = \left(\sqrt[3]{6}\right)^2$$. 8. **Final answer:** $$x = \left(\sqrt[3]{6}\right)^2$$. This means $$x$$ is the square of the cube root of 6.