Question

question

simplify: \\(\sqrt{\frac{81d^9}{25d^4}}\\)

provide your answer below:

Explanation:

Simplify the fraction inside the radical

$$ \frac{81d^9}{25d^4} = \frac{81}{25}d^{9-4} = \frac{81d^5}{25} $$

Apply the quotient property of radicals

$$ \sqrt{\frac{81d^5}{25}} = \frac{\sqrt{81d^5}}{\sqrt{25}} = \frac{\sqrt{81 \cdot d^4 \cdot d}}{5} $$

Simplify the numerator radical

$$ \frac{9d^2\sqrt{d}}{5} $$

Answer:

\(\frac{9d^2\sqrt{d}}{5}\)