Question

Which of the following is equivalent to the radical expression below when

x>0?
√2x √x +3.
OA. √x² + 6x
OB. √2x2 + 3x
OC. √2x² + x
D. √2x² + 6x

Answer 1

the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent. option (C) √(2x² + x) is equivalent to the original expression √(2x) * √(x+3) when x > 0.

Explanation:

To simplify the expression √(2x) * √(x+3), we can use the property of radicals that says:

√(a) * √(b) = √(a * b)

So, we have:

√(2x) * √(x+3) = √(2x * (x+3))

Multiplying out the terms inside the radical, we get:

√(2x * (x+3)) = √(2x² + 6x)

Therefore, the expression √(2x) * √(x+3) is equivalent to the radical expression √(2x² + 6x) when x > 0.

So, the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent:

√(2x² + 6x) = √(2x² + x + 5x) = √(x * (2x + 5)) = √x * √(2x + 5)