Answer: [tex]4x^2\text{ \lparen last option\rparen}[/tex]Explanation:
Given:
[tex]\frac{\sqrt{6x^3}}{\sqrt{3x}}•\text{ }\sqrt{8x^2}[/tex]
To find:
to simplify the expression
To simplify, we will be combining like terms. All the roots are square roots, so we can combine them under one root:
[tex]\begin{gathered} \frac{\sqrt{6x^3}}{\sqrt{3x}}\times\text{ }\sqrt{8x^2}\text{ = }\frac{\sqrt{6x^3\times8x^2}}{\sqrt{3x}} \\ \\ \frac{\sqrt{6x^3\times8x^2}}{\sqrt{3x}}\text{ = }\sqrt{\frac{6x^3\times8x^2}{3x}} \\ \\ =\sqrt{\frac{6\times x^3\times8\times x^2}{3x}}\text{ = }\sqrt{\frac{48\times x^5}{3x}} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{\frac{48\times x^5}{3x}}=\text{ }\sqrt{\frac{48}{3}\times\frac{x^5}{x}} \\ \\ =\text{ }\sqrt{16\times x^4} \\ \\ =\text{ }\sqrt{(4)\placeholder{⬚}^2\times(x^2)\placeholder{⬚}^2}\text{ = }\sqrt{(4x^2)\placeholder{⬚}^2} \\ \\ square\text{ cancels square root:} \\ =\text{ 4x}^2\text{ \lparen1st option\rparen} \end{gathered}[/tex]
