Question

Which expression is equivalent to square root 55x^7 y^6/11x^11 y^8? Assume x > 0 and y > 0.

Answer 1

Answer:

Basically the answer is C.

Answer 2

The first step for solving this expression is to reduce the fraction with 11.
$\sqrt{ \frac{5 x^{7} y^{6} }{ x^{11} y^{8} } }$
Now reduce the fraction with $x^{7}$.
$\sqrt{ \frac{5 y^{6} }{ x^{4} y^{8} } }$
Reduce the fraction one more time with $y^{6}$.
$\sqrt{ \frac{5}{ x^{4} y^{2} } }$
To take the root of a fraction,, we must take the root of the numerator and denominator separately. This rule will change the expression to the following:
$\frac{ \sqrt{5} }{ x^{2} y}$
Since we cannot simplify this fraction any further,, the final answer is going to be $\frac{ \sqrt{5} }{ x^{2} y}$.
Let me know if you have any further questions.
:)