Question

simplify the radical using the product property.

\\\sqrt{125x^3y^{12}}\\

\\\sqrt{125x^3y^{12}} = \box\\
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: Simplifying radical expressions

Step 1: Factor into perfect squares

$$ \sqrt{125x^3y^{12}} = \sqrt{(25 \cdot 5) \cdot (x^2 \cdot x) \cdot (y^{12})} $$

Step 2: Group perfect squares and remaining terms

$$ \sqrt{(25 \cdot x^2 \cdot y^{12}) \cdot (5 \cdot x)} $$

Step 3: Apply the Product Property of Radicals

$$ \sqrt{25x^2y^{12}} \cdot \sqrt{5x} = 5xy^6\sqrt{5x} $$

Answer:

\(5xy^6\sqrt{5x}\)