Algebra Examples

$\sqrt{288 x^{5} y^{3} z^{2}} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $288 x^{5} y^{3} z^{2}$ as ${(12 x^{2} y z)}^{2} \cdot (2 x y)$ .

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Step 1.1.1

Factor $144$ out of $288$ .

$\sqrt{144 (2) x^{5} y^{3} z^{2}} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.2

Rewrite $144$ as $12^{2}$ .

$\sqrt{12^{2} \cdot 2 x^{5} y^{3} z^{2}} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.3

Factor out $x^{4}$ .

$\sqrt{12^{2} \cdot 2 (x^{4} x) y^{3} z^{2}} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.4

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

$\sqrt{12^{2} \cdot 2 ({(x^{2})}^{2} x) y^{3} z^{2}} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.5

Factor out $y^{2}$ .

$\sqrt{12^{2} \cdot 2 ({(x^{2})}^{2} x) (y^{2} y) z^{2}} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.6

Move $y$ .

$\sqrt{12^{2} \cdot 2 ({(x^{2})}^{2} x) (y^{2}) z^{2} y} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.7

Move $x$ .

$\sqrt{(12^{2} \cdot 2 ({(x^{2})}^{2}) (y^{2})) z^{2} x y} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.8

Move $2$ .

$\sqrt{((12^{2} ({(x^{2})}^{2})) (y^{2})) z^{2} \cdot 2 x y} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.9

Rewrite $((12^{2} ({(x^{2})}^{2})) (y^{2})) z^{2}$ as ${(12 x^{2} y z)}^{2}$ .

$\sqrt{{(12 x^{2} y z)}^{2} \cdot 2 x y} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.10

Add parentheses.

$\sqrt{{(12 x^{2} y z)}^{2} \cdot 2 (x y)} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.1.11

Add parentheses.

$\sqrt{{(12 x^{2} y z)}^{2} \cdot (2 x y)} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.2

Pull terms out from under the radical.

$12 x^{2} y z \sqrt{2 x y} + \sqrt{18 x^{5} y^{3} z^{2}}$

Step 1.3

Rewrite $18 x^{5} y^{3} z^{2}$ as ${(3 x^{2} y z)}^{2} \cdot (2 x y)$ .

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Step 1.3.1

Factor $9$ out of $18$ .

$12 x^{2} y z \sqrt{2 x y} + \sqrt{9 (2) x^{5} y^{3} z^{2}}$

Step 1.3.2

Rewrite $9$ as $3^{2}$ .

$12 x^{2} y z \sqrt{2 x y} + \sqrt{3^{2} \cdot 2 x^{5} y^{3} z^{2}}$

Step 1.3.3

Factor out $x^{4}$ .

$12 x^{2} y z \sqrt{2 x y} + \sqrt{3^{2} \cdot 2 (x^{4} x) y^{3} z^{2}}$

Step 1.3.4

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

$12 x^{2} y z \sqrt{2 x y} + \sqrt{3^{2} \cdot 2 ({(x^{2})}^{2} x) y^{3} z^{2}}$

Step 1.3.5

Factor out $y^{2}$ .

$12 x^{2} y z \sqrt{2 x y} + \sqrt{3^{2} \cdot 2 ({(x^{2})}^{2} x) (y^{2} y) z^{2}}$

Step 1.3.6

Move $y$ .

$12 x^{2} y z \sqrt{2 x y} + \sqrt{3^{2} \cdot 2 ({(x^{2})}^{2} x) y^{2} z^{2} y}$

Step 1.3.7

Move $x$ .

$12 x^{2} y z \sqrt{2 x y} + \sqrt{3^{2} \cdot 2 {(x^{2})}^{2} y^{2} z^{2} x y}$

Step 1.3.8

Move $2$ .

$12 x^{2} y z \sqrt{2 x y} + \sqrt{3^{2} {(x^{2})}^{2} y^{2} z^{2} \cdot 2 x y}$

Step 1.3.9

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

$12 x^{2} y z \sqrt{2 x y} + \sqrt{{(3 x^{2} y z)}^{2} \cdot 2 x y}$

Step 1.3.10

Add parentheses.

$12 x^{2} y z \sqrt{2 x y} + \sqrt{{(3 x^{2} y z)}^{2} \cdot 2 (x y)}$

Step 1.3.11

Add parentheses.

$12 x^{2} y z \sqrt{2 x y} + \sqrt{{(3 x^{2} y z)}^{2} \cdot (2 x y)}$

Step 1.4

Pull terms out from under the radical.

$12 x^{2} y z \sqrt{2 x y} + 3 x^{2} y z \sqrt{2 x y}$

Step 2

Add $12 x^{2} y z \sqrt{2 x y}$ and $3 x^{2} y z \sqrt{2 x y}$ .

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