Question

study paths initial diagnostic: tx math bridge - stage 2 tx math bri radical expressions and quadratic equations progress: the movement of the progress bar may be uneven because questions can be worth more or le perform the operations and simplify: \\(\frac{\sqrt{6x^3}}{\sqrt{3x}} \cdot \sqrt{8x^2}\\) \\(\circ\\) \\(4x\sqrt{x^3}\\) \\(\circ\\) \\(16x^4\\) \\(\circ\\) \\(\sqrt{16x^4}\\) \\(\circ\\) \\(4x^2\\) submit pass hold dont know answer skip for now

Explanation:

Step1: Simplify the fraction of radicals

First, simplify \(\frac{\sqrt{6x^3}}{\sqrt{3x}}\). Using the property \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\) (where \(a = 6x^3\) and \(b = 3x\)), we get \(\sqrt{\frac{6x^3}{3x}}\). Simplify the fraction inside the square root: \(\frac{6x^3}{3x}=2x^2\), so this becomes \(\sqrt{2x^2}\).

Step2: Multiply by the other radical

Now we have \(\sqrt{2x^2}\cdot\sqrt{8x^2}\). Using the property \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\), we multiply the radicands: \(2x^2\cdot8x^2 = 16x^4\), so we get \(\sqrt{16x^4}\).

Step3: Simplify the square root

Simplify \(\sqrt{16x^4}\). The square root of 16 is 4, and the square root of \(x^4\) is \(x^2\) (since \((x^2)^2=x^4\)), so \(\sqrt{16x^4}=4x^2\).

Answer:

\(4x^2\) (corresponding to the option "4\(x^2\)")