Question

Apex Which of the choices are equivalent to the quotient below? Check all that apply

Answer 1

Simplify the expression.

$\begin{gathered} \frac{\sqrt[]{100}}{\sqrt[]{20}}=\sqrt[]{\frac{100}{20}} \\ =\sqrt[]{\frac{4\cdot25}{4\cdot5}} \\ =\sqrt[]{\frac{25}{5}} \\ =\frac{\sqrt[]{25}}{\sqrt[]{5}} \end{gathered}$

Simplify the expression further to obtain the value of expression.

$\begin{gathered} \frac{\sqrt[]{100}}{\sqrt[]{20}}=\frac{\sqrt[]{25}}{\sqrt[]{5}} \\ =\frac{5}{\sqrt[]{5}} \\ =\sqrt[]{5} \end{gathered}$

Simplify the expression by multiplcation of square root 3 to numerator and denominator.

$\begin{gathered} \sqrt[]{5}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{\sqrt[]{5\cdot3}}{\sqrt[]{3}} \\ =\frac{\sqrt[]{15}}{\sqrt[]{3}} \end{gathered}$

Thus option A, option C and option F are correct.