Question

Assume x > 0 and y 0.

algebra II engenuity

Answer 1

Third Option

Explanation:

Given expression is:

`\sqrt{(55x^7y^6)/(11x^11y^8)}`

Simplifying

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