We have the following expression:
[tex]3\sqrt[]{45}[/tex]
First, we must find the prime factorization of the number inside the radical:
[tex]45=3\times3\times5[/tex]
Next, determine the index of the radical. In our case the index is two because it is a square root, which means we need two of a kind:
[tex]45=3\times3\times5=3^2\times5[/tex]
Then, we can move 3 outside the radical, that is
[tex]3\sqrt[]{45}=3\sqrt[]{3^2\times5}=3\times3\sqrt[]{5}[/tex]
and finally, simplify the expression both inside and outside the radical:
[tex]3\sqrt[]{45}=9\sqrt[]{5}[/tex]
Then, the answer is
