Question

Which expression is equivalent to sqrt 128x^5y^6/2x^7y^5

Answer 1

$\sqrt{\dfrac{128x^5y^6}{2x^7y^5}}=\sqrt{\dfrac{128}{2}\cdot\dfrac{x^5}{x^7}\cdot\dfrac{y^6}{y^5}}=\sqrt{64\cdot\dfrac{1}{x^2}\cdot\dfrac{y}{1}}=\sqrt{64}\cdot\sqrt{\dfrac{1}{x^2}}\cdot\sqrt{y}\\\\=\boxed{\dfrac{8\sqrt{y}}{|x|}}\\\\Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=|a|$