Precalculus Examples

$\sqrt{28 y^{8} z^{5}}$

Step 1

Rewrite $28 y^{8} z^{5}$ as ${(2 y^{4} z^{2})}^{2} \cdot (7 z)$ .

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Step 1.1

Factor $4$ out of $28$ .

$\sqrt{4 (7) y^{8} z^{5}}$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 7 y^{8} z^{5}}$

Step 1.3

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

$\sqrt{2^{2} \cdot 7 {(y^{4})}^{2} z^{5}}$

Step 1.4

Factor out $z^{4}$ .

$\sqrt{2^{2} \cdot 7 {(y^{4})}^{2} (z^{4} z)}$

Step 1.5

Rewrite $z^{4}$ as ${(z^{2})}^{2}$ .

$\sqrt{2^{2} \cdot 7 {(y^{4})}^{2} ({(z^{2})}^{2} z)}$

Step 1.6

Move $7$ .

$\sqrt{2^{2} {(y^{4})}^{2} {(z^{2})}^{2} \cdot 7 z}$

Step 1.7

Rewrite $2^{2} {(y^{4})}^{2} {(z^{2})}^{2}$ as ${(2 y^{4} z^{2})}^{2}$ .

$\sqrt{{(2 y^{4} z^{2})}^{2} \cdot 7 z}$

Step 1.8

Add parentheses.

$\sqrt{{(2 y^{4} z^{2})}^{2} \cdot (7 z)}$

Step 2

Pull terms out from under the radical.

$2 y^{4} z^{2} \sqrt{7 z}$