Algebra Examples

$\sqrt{8 a^{2}} \cdot \sqrt{4 a}$

Step 1

Rewrite $8 a^{2}$ as ${(2 a)}^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) a^{2}} \cdot \sqrt{4 a}$

Step 1.2

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

$\sqrt{2^{2} \cdot 2 a^{2}} \cdot \sqrt{4 a}$

Step 1.3

Move $2$ .

$\sqrt{2^{2} a^{2} \cdot 2} \cdot \sqrt{4 a}$

Step 1.4

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

$\sqrt{{(2 a)}^{2} \cdot 2} \cdot \sqrt{4 a}$

$\sqrt{{(2 a)}^{2} \cdot 2} \cdot \sqrt{4 a}$

Step 2

Pull terms out from under the radical.

$2 a \sqrt{2} \cdot \sqrt{4 a}$

Step 3

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

$2 a \sqrt{2} \cdot \sqrt{2^{2} a}$

Step 4

Pull terms out from under the radical.

$2 a \sqrt{2} \cdot (2 \sqrt{a})$

Step 5

Multiply $2 a \sqrt{2} (2 \sqrt{a})$ .

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Step 5.1

Multiply $2$ by $2$ .

$4 a \sqrt{2} \sqrt{a}$

Step 5.2

Combine using the product rule for radicals.

$4 a \sqrt{a \cdot 2}$

$4 a \sqrt{a \cdot 2}$

Step 6

Reorder factors in $4 a \sqrt{a \cdot 2}$ .

$4 a \sqrt{2 a}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$