Question

Find square root of 45 * square root of 20 by prime factorisation method

Answer 1

$$\begin{gathered} \sqrt{45}\times \sqrt{20} \\ =\sqrt{3\times 3\times 5}\times \sqrt{2\times 2\times 5} \\ =\sqrt{3\times 3\times 5\times 2\times 2\times 5} \\ =\sqrt{2\times 2\times 3\times 3\times 5\times 5} \\ =2\times 3\times 5 \\ =30 \end{gathered}$$