Question

Which choice is equivalent to the expression below when x is greater than or equal to 0?

Answer 1

Choice A is the correct answer

Explanation:

`2x√(2x)`

Find the attachment below for the explanation

Answer 2

For this case we must indicate an expression equivalent to:

`\sqrt {18x ^ 3} - \sqrt {9x ^ 3} +3 \sqrt {x ^ 3} - \sqrt {2x ^ 3}`

So, rewriting the terms within the roots we have:

`18x ^ 3 = (3x) ^ 2 * (2x)\\9x ^ 3 = (3x) ^ 2 * (x)\\x ^ 3 = x ^ 2 * x\\2x ^ 3 = (2x) * x ^ 2`

So:

`\sqrt {(3x) ^ 2 * (2x)} - \sqrt {(3x) ^ 2 * (x)} + 3 \sqrt {x ^ 2 * x} - \sqrt {(2x) * x ^ 2} =`

Removing the terms of the radical:

`3x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} -x \sqrt {2x} =`

We simplify adding terms:

`3x \sqrt {2x} -x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} =\\2x \sqrt {2x} + 0 =\\2x \sqrt {2x}`

Answer:

Option A