Question

Which choice is equivalent to the quotient shown here when x>0?

Answer 1

$\sqrt{22x^6}:\sqrt{11x^4}=\dfrac{\sqrt{22x^6}}{\sqrt{11x^4}}=\sqrt{\dfrac{22}{11}x^{6-4}}=\sqrt{2x^2}=\sqrt2\cdot\sqrt{x^2}=x\sqrt2\\\\Answer:\ \boxed{c.\ x\sqrt2}\\\\Used:\\\\\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\\sqrt{a^2}=a$