Question

select the correct answer. which expression is equivalent to \\(sqrt{48x^5}\\) if \\(x > 0\\)? a. \\(12x^3sqrt{3x}\\) b. \\(4x^3sqrt{3}\\) c. \\(4x^2sqrt{3x}\\) d. \\(12x^2sqrt{x}\\)

Explanation:

Step1: Factor the radicand

$\sqrt{48x^5} = \sqrt{16 \times 3 \times x^4 \times x}$

Step2: Simplify perfect squares

$\sqrt{16} \times \sqrt{x^4} \times \sqrt{3x} = 4x^2\sqrt{3x}$

Answer:

C. $4x^2\sqrt{3x}$