Question

select the correct answer.

which expression is equivalent to \\(\frac{12y}{\sqrt{2y}}\\), if \\(y > 0\\)?

\\(12y\sqrt{2y}\\)

\\(6\sqrt{y}\\)

\\(12y\\)

\\(6\sqrt{2y}\\)

Explanation:

Write the expression

$$ \frac{12y}{\sqrt{2y}},\quad y > 0 $$

Rationalize the denominator

$$ \frac{12y}{\sqrt{2y}} \cdot \frac{\sqrt{2y}}{\sqrt{2y}} = \frac{12y\sqrt{2y}}{2y} $$

Simplify the expression

$$ \frac{12y\sqrt{2y}}{2y} = 6\sqrt{2y} $$

Answer:

• (A) \(12y\sqrt{2y}\)
• (B) \(6\sqrt{y}\)
• (C) \(12y\)
• (D) \(6\sqrt{2y}\) (Correct answer)