Pre-Algebra Examples

$\sqrt{8 x^{4} y^{4}} + \sqrt{12 x^{4} y^{4}}$

Step 1

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

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Step 1.1

Factor $4$ out of $8$ .

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

Step 1.2

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

$\sqrt{2^{2} \cdot 2 x^{4} y^{4}} + \sqrt{12 x^{4} y^{4}}$

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Move $2$ .

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

Step 1.6

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

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

Step 2

Pull terms out from under the radical.

$2 x^{2} y^{2} \sqrt{2} + \sqrt{12 x^{4} y^{4}}$

Step 3

Rewrite $12 x^{4} y^{4}$ as ${(2 x^{2} y^{2})}^{2} \cdot 3$ .

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Step 3.1

Factor $4$ out of $12$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

Move $3$ .

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

Step 3.6

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

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

Step 4

Pull terms out from under the radical.

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