Question

Hi can you help me with this question? Thank you

Answer 1

Answer:
`4x^2\text{ \lparen last option\rparen}`Step-by-step explanation:

Given:

`(√(6x^3))/(√(3x))•\text{ }√(8x^2)`

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:

`\begin{gathered} (√(6x^3))/(√(3x))*\text{ }√(8x^2)\text{ = }(√(6x^3*8x^2))/(√(3x)) \\ \\ (√(6x^3*8x^2))/(√(3x))\text{ = }\sqrt{(6x^3*8x^2)/(3x)} \\ \\ =\sqrt{(6* x^3*8* x^2)/(3x)}\text{ = }\sqrt{(48* x^5)/(3x)} \end{gathered}`
`\begin{gathered} \sqrt{(48* x^5)/(3x)}=\text{ }\sqrt{(48)/(3)*(x^5)/(x)} \\ \\ =\text{ }√(16* x^4) \\ \\ =\text{ }\sqrt{(4)\placeholder{⬚}^2*(x^2)\placeholder{⬚}^2}\text{ = }\sqrt{(4x^2)\placeholder{⬚}^2} \\ \\ square\text{ cancels square root:} \\ =\text{ 4x}^2\text{ \lparen1st option\rparen} \end{gathered}`