Answer :
First let's see what we got
[tex]\sqrt{200}=\sqrt{100*2}=10\sqrt{2}[/tex]
and
[tex]\sqrt{32}=\sqrt{2^5}=\sqrt{2^4*2}=4\sqrt{2}[/tex]
then
[tex](3\sqrt{200})*(4\sqrt{32})[/tex]
replacing
[tex]3*(10\sqrt{2})*(4*4\sqrt{2})[/tex]
[tex]30\sqrt{2}*16\sqrt{2}[/tex]
[tex]480*\sqrt{2}*\sqrt{2}[/tex]
[tex]480*2[/tex]
[tex]\boxed{\boxed{960}}[/tex]
[tex]\sqrt{200}=\sqrt{100*2}=10\sqrt{2}[/tex]
and
[tex]\sqrt{32}=\sqrt{2^5}=\sqrt{2^4*2}=4\sqrt{2}[/tex]
then
[tex](3\sqrt{200})*(4\sqrt{32})[/tex]
replacing
[tex]3*(10\sqrt{2})*(4*4\sqrt{2})[/tex]
[tex]30\sqrt{2}*16\sqrt{2}[/tex]
[tex]480*\sqrt{2}*\sqrt{2}[/tex]
[tex]480*2[/tex]
[tex]\boxed{\boxed{960}}[/tex]
[tex](3 \sqrt{200}) \cdot (4 \sqrt{32})=(3 \sqrt{100\cdot 2}) \cdot (4 \sqrt{16\cdot 2})=(3 \cdot \sqrt{100 }\cdot \sqrt{2}) \cdot (4 \cdot \sqrt{16 }\cdot \sqrt{2})=\\ \\= ( 3 \cdot 10\cdot \sqrt{2}) \cdot (4\cdot 4\cdot \sqrt{2})= 3 \cdot 10 \cdot 4\cdot 4\cdot \sqrt{2} \cdot \sqrt{2}=480\cdot \sqrt{2\cdot 2}=\\ \\=480\cdot \sqrt{4}=480\cdot 2=960[/tex]
