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

Accepted Solution

The first step for solving this expression is to reduce the fraction with 11.
[tex] \sqrt{ \frac{5 x^{7} y^{6} }{ x^{11} y^{8} } } [/tex]
Now reduce the fraction with [tex] x^{7} [/tex]
[tex] \sqrt{ \frac{5 y^{6} }{ x^{4} y^{8} } } [/tex]
Reduce the fraction with [tex] y^{6} [/tex]
[tex] \sqrt{ \frac{5}{ x^{4} y^{2} } } [/tex]
Lastly,, we need to remember our radical rules. They state that in order for us to take a root of a fraction,, we must take the root of the numerator and denominator separately. Knowing this rule,, this changes the expression to the following:
[tex] \frac{ \sqrt{5} }{ x^{2} y} [/tex]
Since we cannot simplify the expression any further,, the correct answer to your question is going to be [tex] \frac{ \sqrt{5} }{ x^{2} y} [/tex],, or option C.
Let me know if you have any further questions.