Pre-Algebra Examples

$\sqrt{252 x^{5} y^{7} z^{3}}$

Step 1

Rewrite $252 x^{5} y^{7} z^{3}$ as ${(6 x^{2} y^{3} z)}^{2} \cdot (7 x y z)$ .

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Step 1.1

Factor $36$ out of $252$ .

$\sqrt{36 (7) x^{5} y^{7} z^{3}}$

Step 1.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 7 x^{5} y^{7} z^{3}}$

Step 1.3

Factor out $x^{4}$ .

$\sqrt{6^{2} \cdot 7 (x^{4} x) y^{7} z^{3}}$

Step 1.4

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

$\sqrt{6^{2} \cdot 7 ({(x^{2})}^{2} x) y^{7} z^{3}}$

Step 1.5

Factor out $y^{6}$ .

$\sqrt{6^{2} \cdot 7 ({(x^{2})}^{2} x) (y^{6} y) z^{3}}$

Step 1.6

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$\sqrt{6^{2} \cdot 7 ({(x^{2})}^{2} x) ({(y^{3})}^{2} y) z^{3}}$

Step 1.7

Factor out $z^{2}$ .

$\sqrt{6^{2} \cdot 7 ({(x^{2})}^{2} x) ({(y^{3})}^{2} y) (z^{2} z)}$

Step 1.8

Move $y$ .

$\sqrt{6^{2} \cdot 7 ({(x^{2})}^{2} x) ({(y^{3})}^{2}) z^{2} y z}$

Step 1.9

Move $x$ .

$\sqrt{(6^{2} \cdot 7 ({(x^{2})}^{2}) ({(y^{3})}^{2})) z^{2} x y z}$

Step 1.10

Move $7$ .

$\sqrt{((6^{2} ({(x^{2})}^{2})) ({(y^{3})}^{2})) z^{2} \cdot 7 x y z}$

Step 1.11

Rewrite $((6^{2} ({(x^{2})}^{2})) ({(y^{3})}^{2})) z^{2}$ as ${(6 x^{2} y^{3} z)}^{2}$ .

$\sqrt{{(6 x^{2} y^{3} z)}^{2} \cdot 7 x y z}$

Step 1.12

Add parentheses.

$\sqrt{{(6 x^{2} y^{3} z)}^{2} \cdot 7 x (y z)}$

Step 1.13

Add parentheses.

$\sqrt{{(6 x^{2} y^{3} z)}^{2} \cdot 7 (x (y z))}$

Step 1.14

Add parentheses.

$\sqrt{{(6 x^{2} y^{3} z)}^{2} \cdot (7 x y z)}$

Step 2

Pull terms out from under the radical.

$6 x^{2} y^{3} z \sqrt{7 x y z}$