Question

what is \frac{\sqrt{25x^2y^2}}{\sqrt{xy}} in simplest form? assume x \ge 0 and y \ge 0.

• 5\sqrt{xy}
• 25\sqrt{xy}
• \sqrt{5xy}
• 5xy\sqrt{xy}

Explanation:

Apply the quotient property of radicals

Using the Quotient Property of Radicals knowledge point

$$ \frac{\sqrt{25x^2y^2}}{\sqrt{xy}} = \sqrt{\frac{25x^2y^2}{xy}} $$

Simplify the expression inside the radical

Using the Radical Simplification knowledge point

$$ \sqrt{\frac{25x^2y^2}{xy}} = \sqrt{25xy} $$

Extract perfect squares from the radical

Using the Radical Simplification knowledge point

$$ \sqrt{25xy} = \sqrt{25} \cdot \sqrt{xy} = 5\sqrt{xy} $$

Answer:

• (A) \(5\sqrt{xy}\) (Correct answer)
• (B) \(25\sqrt{xy}\)
• (C) \(\sqrt{5xy}\)
• (D) \(5xy\sqrt{xy}\)