[tex]\sqrt{22x^6}:\sqrt{11x^4}=\dfrac{\sqrt{22x^6}}{\sqrt{11x^4}}=\sqrt{\dfrac{22}{11}x^{6-4}}=\sqrt{2x^2}=\sqrt2\cdot\sqrt{x^2}=x\sqrt2\\\\Answer:\ \boxed{c.\ x\sqrt2}\\\\Used:\\\\\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\\sqrt{a^2}=a[/tex]
The equation is equivalent to the quotient [tex]\rm x\sqrt{2}[/tex].
The correct option is c.
Given
Equation; [tex]\rm \sqrt{\dfrac{22x^6}{11x^4}}[/tex]
The following properties are used to solve the equation is;
[tex]\rm \sqrt{\dfrac{a}{b}} =\dfrac{\sqrt{a}}{\sqrt{b}}\\\\[/tex]
[tex]\rm \dfrac{a^m}{a^n}=a^{m-n}\\\\\sqrt{a^2} =a[/tex]
Then,
The equation is equivalent to;
[tex]\rm =\sqrt{\dfrac{22x^6}{11x^4}}\\\\\rm= \sqrt{\dfrac{22 \times x^6}{11\times x^4}}\\\\\rm =\sqrt{\dfrac{2\times x^6}{x^4}}\\\\\rm= \sqrt{2\times x^{6-4}}\\\\=\sqrt{2x^2} \\\\=\sqrt{2}\\\\ =x\sqrt{2}[/tex]
Hence, the equation is equivalent to the quotient [tex]\rm x\sqrt{2}[/tex].
To know more square root properties click the link given below.
https://brainly.com/question/9956052
