Simplify square root of (5-x)^3-8

$\sqrt{{(5 - x)}^{3}} - 8$

Simplify each term.

Factor out ${(5 - x)}^{2}$ .

$\sqrt{{(5 - x)}^{2} (5 - x)} - 8$

Pull terms out from under the radical.

$(5 - x) \sqrt{5 - x} - 8$

Apply the distributive property.

$5 \sqrt{5 - x} - x \sqrt{5 - x} - 8$

$5 \sqrt{5 - x} - x \sqrt{5 - x} - 8$

Simplify with commuting.

Reorder $5$ and $- x$ .

$5 \sqrt{- x + 5} - x \sqrt{5 - x} - 8$

Reorder $5$ and $- x$ .

$5 \sqrt{- x + 5} - x \sqrt{- x + 5} - 8$

$5 \sqrt{- x + 5} - x \sqrt{- x + 5} - 8$

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