Question

using the quotient property of radicals
what is \\(\frac{\sqrt{12x^8}}{\sqrt{3x^2}}\\) in simplest form, where \\(x \geq 0\\)?
\\(2\sqrt{3}x^4\\)
\\(\sqrt{15x^5}\\)
\\(2x^2\\)
\\(2x^3\\)

Explanation:

Step1: Apply Quotient Property

$\frac{\sqrt{12x^8}}{\sqrt{3x^4}} = \sqrt{\frac{12x^8}{3x^4}}$

Step2: Simplify the radicand

$\sqrt{\frac{12}{3} \cdot \frac{x^8}{x^4}} = \sqrt{4x^4}$

Step3: Simplify the square root

$\sqrt{4x^4} = \sqrt{4} \cdot \sqrt{x^4} = 2x^2$

Answer:

$2x^2$ (Option: $2x^2$)