Simplify. All Variables represent (3√200)*(4√32)

First let’s see what we got

\( \sqrt{200}=\sqrt{100*2}=10\sqrt{2} \)

and

\( \sqrt{32}=\sqrt{2^5}=\sqrt{2^4*2}=4\sqrt{2} \)

then

\( (3\sqrt{200})*(4\sqrt{32}) \)

replacing

\( 3*(10\sqrt{2})*(4*4\sqrt{2}) \)

\( 30\sqrt{2}*16\sqrt{2} \)

\( 480*\sqrt{2}*\sqrt{2} \)

\( 480*2 \)

\( \boxed{\boxed{960}} \)

\( (3 \sqrt{200}) \cdot (4 \sqrt{32})=(3 \sqrt{100\cdot 2}) \cdot (4 \sqrt{16\cdot 2})=(3 \cdot \sqrt{100 }\cdot \sqrt{2}) \cdot (4 \cdot \sqrt{16 }\cdot \sqrt{2})=\\ \\= ( 3 \cdot 10\cdot \sqrt{2}) \cdot (4\cdot 4\cdot \sqrt{2})= 3 \cdot 10 \cdot 4\cdot 4\cdot \sqrt{2} \cdot \sqrt{2}=480\cdot \sqrt{2\cdot 2}=\\ \\=480\cdot \sqrt{4}=480\cdot 2=960 \)

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