1. **State the problem:** Simplify the expression $\sqrt{8} - \sqrt{x} \sqrt{60}$. 2. **Recall the property of square roots:** $\sqrt{a} \sqrt{b} = \sqrt{ab}$. This allows us to combine the roots in the second term. 3. **Apply the property:** $\sqrt{x} \sqrt{60} = \sqrt{60x}$. So the expression becomes $\sqrt{8} - \sqrt{60x}$. 4. **Simplify $\sqrt{8}$:** $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \sqrt{2} = 2\sqrt{2}$. 5. **Rewrite the expression:** $2\sqrt{2} - \sqrt{60x}$. 6. **Simplify $\sqrt{60x}$ if possible:** $\sqrt{60x} = \sqrt{4 \times 15x} = \sqrt{4} \sqrt{15x} = 2\sqrt{15x}$. 7. **Final simplified expression:** $2\sqrt{2} - 2\sqrt{15x}$. This is the simplified form of the original expression.