To multiply $\sqrt{10}$ and $\sqrt{15}$, multiply the numbers under the square root.
$$\sqrt{150}$$
Factor $150=5^{2}\times 6$. Rewrite the square root of the product $\sqrt{5^{2}\times 6}$ as the product of square roots $\sqrt{5^{2}}\sqrt{6}$. Take the square root of $5^{2}$.
