Question

Assume x > 0 and y 0.algebra II engenuity

Answer 1

Answer:

Third Option

Step-by-step explanation:

Given expression is:

$\sqrt{\frac{55x^7y^6}{11x^11y^8}}$

Simplifying

$=\sqrt{\frac{11*5*x^7*y^6}{11*x^11*y^8}}\\=\sqrt{\frac{5*x^7*y^6}{x^11*y^8}}\\Combining\ exponents\ with\ same\ base\\=\sqrt{\frac{5}{11*x^{(11-7)}*y^{(8-6)}}}\\=\sqrt{\frac{5}{x^{4}*y^{2}}}\\Applying\ radical\\=\frac{5^{\frac{1}{2}}}{x^{(4*\frac{1}{2})}*y^{(2*\frac{1}{2})}}}\\=\frac{\sqrt{5}}{x^2y}$

As 5 cannot be taken out of the square root, it will remain inside the square root.

Hence, Third option is the correct answer ..