1. **State the problem:** We need to find the value of $x$ given the equation $x \times x = 6000m$. 2. **Rewrite the equation:** The equation can be written as $x^2 = 6000m$. 3. **Formula used:** To solve for $x$, we take the square root of both sides: $$x = \sqrt{6000m}$$. 4. **Important rule:** When taking the square root of both sides, remember that $x$ can be positive or negative, so $$x = \pm \sqrt{6000m}$$. 5. **Calculate the square root:** Simplify $\sqrt{6000m}$. 6. **Factor inside the square root:** $$\sqrt{6000m} = \sqrt{6000} \times \sqrt{m}$$. 7. **Simplify $\sqrt{6000}$:** $$6000 = 100 \times 60$$ $$\sqrt{6000} = \sqrt{100 \times 60} = \sqrt{100} \times \sqrt{60} = 10 \times \sqrt{60}$$ 8. **Simplify $\sqrt{60}$:** $$60 = 4 \times 15$$ $$\sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2 \times \sqrt{15}$$ 9. **Combine all:** $$x = \pm 10 \times 2 \times \sqrt{15} \times \sqrt{m} = \pm 20 \sqrt{15m}$$ **Final answer:** $$x = \pm 20 \sqrt{15m}$$