Question

select the correct answer.

which expression is equivalent to (3xy^3sqrt{2x})?

(sqrt{6x^2y^3})

(sqrt{6x^3y^6})

(sqrt{18x^2y^3})

(sqrt{18x^3y^6})

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Rewrite the coefficient as a radical

To move the outside terms inside the square root, square them:

$$ (3xy^3)^2 = 3^2 \cdot x^2 \cdot (y^3)^2 = 9x^2y^6 $$

This means:

$$ 3xy^3 = \sqrt{9x^2y^6} $$

Step 2: Multiply the radicals

Combine the terms under a single square root:

$$ 3xy^3\sqrt{2x} = \sqrt{9x^2y^6} \cdot \sqrt{2x} $$

$$ = \sqrt{9x^2y^6 \cdot 2x} $$

$$ = \sqrt{18x^3y^6} $$

Answer:

$$ \sqrt{18x^3y^6} $$

(the fourth option)