Simplify square root of 125t^16

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Trigonometry

$\sqrt{125 t^{16}}$

Rewrite $125 t^{16}$ as ${(5 t^{8})}^{2} \cdot 5$ .

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Factor $25$ out of $125$ .

$\sqrt{25 (5) t^{16}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 5 t^{16}}$

Rewrite $t^{16}$ as ${(t^{8})}^{2}$ .

$\sqrt{5^{2} \cdot 5 {(t^{8})}^{2}}$

Move $5$ .

$\sqrt{5^{2} {(t^{8})}^{2} \cdot 5}$

Rewrite $5^{2} {(t^{8})}^{2}$ as ${(5 t^{8})}^{2}$ .

$\sqrt{{(5 t^{8})}^{2} \cdot 5}$

Pull terms out from under the radical.

$5 t^{8} \sqrt{5}$

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