Question

current objective
use the quotient property to simplify square roots

question

simplify: \\(\sqrt{\frac{448u^3y^3}{900u^2y^{11}}}\\).

provide your answer below:

Explanation:

Simplify the fraction inside the radical

$$ \frac{448u^3y^3}{900u^2y^{11}} = \frac{448}{900} \cdot \frac{u^3}{u^2} \cdot \frac{y^3}{y^{11}} = \frac{112}{225} \cdot u \cdot \frac{1}{y^8} = \frac{112u}{225y^8} $$

Apply the quotient property of square roots

$$ \sqrt{\frac{112u}{225y^8}} = \frac{\sqrt{112u}}{\sqrt{225y^8}} $$

Simplify the numerator and denominator radicals

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Answer:

\(\frac{4\sqrt{7u}}{15y^4}\)