Question

The value of $\sqrt{99}\times \sqrt{396}$ is

Answer 1

We know that $\sqrt{\text{a}}\times \sqrt{\text{b}}=\sqrt{\text{ab}}(\text{here a,b≥0)}$

First we write the prime factorization of the given numbers

$$\begin{gathered} 99=3\times 3\times 11 \\ 396=2\times 2\times 3\times 3\times 11 \end{gathered}$$

Therefore, $\sqrt{99}\times \sqrt{396}=\sqrt{99\times 396}=\sqrt{3\times 3\times 11\times 2\times 2\times 3\times 3\times 11}$$=3\times 2\times 3\times 11=198$