Precalculus Examples

$\sqrt[4]{81 r^{5} s^{8}}$

Step 1

Rewrite $81 r^{5} s^{8}$ as ${(3 r s^{2})}^{4} r$ .

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Step 1.1

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} r^{5} s^{8}}$

Step 1.2

Factor out $r^{4}$ .

$\sqrt[4]{3^{4} (r^{4} r) s^{8}}$

Step 1.3

Rewrite $s^{8}$ as ${(s^{2})}^{4}$ .

$\sqrt[4]{3^{4} (r^{4} r) {(s^{2})}^{4}}$

Step 1.4

Move $r$ .

$\sqrt[4]{3^{4} (r^{4}) {(s^{2})}^{4} r}$

Step 1.5

Rewrite $3^{4} (r^{4}) {(s^{2})}^{4}$ as ${(3 r s^{2})}^{4}$ .

$\sqrt[4]{{(3 r s^{2})}^{4} r}$

Step 2

Pull terms out from under the radical.

$3 r s^{2} \sqrt[4]{r}$