Answer:
C. x√2
Explanation:
Given the quotient:
[tex]\sqrt{14x^3}\div\sqrt{7x}[/tex]
We can write the division as one quotient as follows:
[tex]=\sqrt{\frac{14x^3}{7x}}[/tex]
Next, we simplify:
[tex]\begin{gathered} =\sqrt{\frac{14}{7}\times\frac{x^3}{x}} \\ =\sqrt{2\times x^2} \end{gathered}[/tex]
We can then separate the product:
[tex]\begin{gathered} =\sqrt{2}\times\sqrt{x^2} \\ =\sqrt{2}\times x \\ =x\sqrt{2} \end{gathered}[/tex]
The equivalent choice is Option C.
