Pre-Algebra Examples

$\sqrt{60 x^{3} y^{4} z}$

Step 1

Rewrite $60 x^{3} y^{4} z$ as ${(2 x y^{2})}^{2} \cdot (15 x z)$ .

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Step 1.1

Factor $4$ out of $60$ .

$\sqrt{4 (15) x^{3} y^{4} z}$

Step 1.2

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

$\sqrt{2^{2} \cdot 15 x^{3} y^{4} z}$

Step 1.3

Factor out $x^{2}$ .

$\sqrt{2^{2} \cdot 15 (x^{2} x) y^{4} z}$

Step 1.4

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

$\sqrt{2^{2} \cdot 15 (x^{2} x) {(y^{2})}^{2} z}$

Step 1.5

Move $x$ .

$\sqrt{2^{2} \cdot 15 (x^{2}) {(y^{2})}^{2} x z}$

Step 1.6

Move $15$ .

$\sqrt{2^{2} (x^{2}) {(y^{2})}^{2} \cdot 15 x z}$

Step 1.7

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

$\sqrt{{(2 x y^{2})}^{2} \cdot 15 x z}$

Step 1.8

Add parentheses.

$\sqrt{{(2 x y^{2})}^{2} \cdot 15 (x z)}$

Step 1.9

Add parentheses.

$\sqrt{{(2 x y^{2})}^{2} \cdot (15 x z)}$

Step 2

Pull terms out from under the radical.

$2 x y^{2} \sqrt{15 x z}$