Question

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

Answer 1

First let's see what we got


`√(200)=√(100*2)=10√(2)`

and


`√(32)=√(2^5)=√(2^4*2)=4√(2)`

then


`(3√(200))*(4√(32))`

replacing


`3*(10√(2))*(4*4√(2))`


`30√(2)*16√(2)`


`480*√(2)*√(2)`


`480*2`


`\boxed{\boxed{960}}`

Answer 2

`(3 √(200)) \cdot (4 √(32))=(3 √(100\cdot 2)) \cdot (4 √(16\cdot 2))=(3 \cdot √(100 )\cdot √(2)) \cdot (4 \cdot √(16 )\cdot √(2))=\\ \\= ( 3 \cdot 10\cdot √(2)) \cdot (4\cdot 4\cdot √(2))= 3 \cdot 10 \cdot 4\cdot 4\cdot √(2) \cdot √(2)=480\cdot √(2\cdot 2)=\\ \\=480\cdot √(4)=480\cdot 2=960`