Algebra Examples

$\sqrt{48 x^{2} y^{5} z}$

Step 1

Rewrite $48 x^{2} y^{5} z$ as ${(4 x y^{2})}^{2} \cdot (3 y z)$ .

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Step 1.1

Factor $16$ out of $48$ .

$\sqrt{16 (3) x^{2} y^{5} z}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 3 x^{2} y^{5} z}$

Step 1.3

Factor out $y^{4}$ .

$\sqrt{4^{2} \cdot 3 x^{2} (y^{4} y) z}$

Step 1.4

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

$\sqrt{4^{2} \cdot 3 x^{2} ({(y^{2})}^{2} y) z}$

Step 1.5

Move $3$ .

$\sqrt{4^{2} x^{2} {(y^{2})}^{2} \cdot 3 y z}$

Step 1.6

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

$\sqrt{{(4 x y^{2})}^{2} \cdot 3 y z}$

Step 1.7

Add parentheses.

$\sqrt{{(4 x y^{2})}^{2} \cdot 3 (y z)}$

Step 1.8

Add parentheses.

$\sqrt{{(4 x y^{2})}^{2} \cdot (3 y z)}$

Step 2

Pull terms out from under the radical.

$| 4 x y^{2} | \sqrt{3 y z}$

Step 3

Remove non-negative terms from the absolute value.

$4 y^{2} | x | \sqrt{3 y z}$