For this case we must indicate an expression equivalent to:
[tex]\sqrt {18x ^ 3} - \sqrt {9x ^ 3} +3 \sqrt {x ^ 3} - \sqrt {2x ^ 3}[/tex]
So, rewriting the terms within the roots we have:
[tex]18x ^ 3 = (3x) ^ 2 * (2x)\\9x ^ 3 = (3x) ^ 2 * (x)\\x ^ 3 = x ^ 2 * x\\2x ^ 3 = (2x) * x ^ 2[/tex]
So:
[tex]\sqrt {(3x) ^ 2 * (2x)} - \sqrt {(3x) ^ 2 * (x)} + 3 \sqrt {x ^ 2 * x} - \sqrt {(2x) * x ^ 2} =[/tex]
Removing the terms of the radical:
[tex]3x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} -x \sqrt {2x} =[/tex]
We simplify adding terms:
[tex]3x \sqrt {2x} -x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} =\\2x \sqrt {2x} + 0 =\\2x \sqrt {2x}[/tex]
Answer:
Option A
