Algebra Examples

$(\sqrt{8 x^{4} y^{2}}) (\sqrt{12 x^{4} y^{2}})$

Step 1

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

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Step 1.1

Factor $4$ out of $8$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Move $2$ .

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

Step 1.5

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Factor $4$ out of $12$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Move $3$ .

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

Step 3.5

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 5.1

Move $x^{2}$ .

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

Step 5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 5.3

Add $2$ and $2$ .

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

Step 6

Multiply $y$ by $y$ by adding the exponents.

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Step 6.1

Move $y$ .

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

Step 6.2

Multiply $y$ by $y$ .

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

Step 7

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

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Step 7.1

Multiply $2$ by $2$ .

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

Step 7.2

Combine using the product rule for radicals.

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

Step 7.3

Multiply $3$ by $2$ .

$4 x^{4} y^{2} \sqrt{6}$