Factor $45=3^{2}\times 5$. Rewrite the square root of the product $\sqrt{3^{2}\times 5}$ as the product of square roots $\sqrt{3^{2}}\sqrt{5}$. Take the square root of $3^{2}$.
Factor $24=2^{2}\times 6$. Rewrite the square root of the product $\sqrt{2^{2}\times 6}$ as the product of square roots $\sqrt{2^{2}}\sqrt{6}$. Take the square root of $2^{2}$.
Consider $\left(3\sqrt{5}-2\sqrt{6}\right)\left(3\sqrt{5}+2\sqrt{6}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
