At what distance (in metre) from the centre of the Moon, the...

Let X be the distance of the point from the centre of earth where gravitational intensity is zero. Therefore, $\frac{\mathrm{GM}_{\mathrm{e}}}{\mathrm{x}^2}=\frac{\mathrm{GM}_{\mathrm{m}}}{\left(3.85 \times 10^8-\mathrm{x}\right)^2} or$\frac{\mathrm{x}}{3.85 \times 10^8-\mathrm{x}}=\sqrt{\frac{\mathrm{M}_{\mathrm{e}}}{\mathrm{M}_{\mathrm{m}}}}=\sqrt{\frac{5.98 \times 10^{24}}{7.35 \times 10^{22}}} \cong 9 or $\quad \frac{x}{9}+x=3.85 \times 10^8$ or $\quad \mathrm{x}=9 \times 3.85 \times 10^8 / 10=3.46 \times 10^8 \mathrm{~m}$ Distance from Moon $=3.85 \times 10^8-3.46 \times 10^8$ $=3.9 \times 10^7 \mathrm{~m} \cong 3.85 \times 10^7 \mathrm{~m}$