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Simplify $\sqrt{75f^9}$ assuming $f$ is greater than or equal to $0$ .

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Simplify radical expressions: mixed review

Full solution

Q. Simplify

\sqrt{75f^9}

assuming

f

is greater than or equal to

0

.

Prime factorize $75$ : $\sqrt{75}f^9$ Prime factorize $75$ . $75 = 3 \times 5 \times 5$
Group identical factors: $\sqrt{3 \cdot 5^2 \cdot f^9}$ Group the identical factors.
Use product property: $\sqrt{3 \cdot 5^2 \cdot f^9}$
Use the product property of radicals.
$\sqrt{3 \cdot 5^2 \cdot f^9} = \sqrt{3} \cdot \sqrt{5^2} \cdot \sqrt{f^9}$
Simplify square roots: $\sqrt{3} \times \sqrt{5^2} \times \sqrt{f^9}$ Simplify the square roots. $\sqrt{5^2} = 5$ and $\sqrt{f^9} = f^{9/2}$
Combine terms: $\sqrt{3} \cdot 5 \cdot f^{\frac{9}{2}}$ Combine the terms. $5 \cdot f^{\frac{9}{2}} \cdot \sqrt{3}$

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