Algebra Examples

$\sqrt{4 x^{2}} \cdot \sqrt{20 x^{2}}$

Step 1

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

$\sqrt{{(2 x)}^{2}} \cdot \sqrt{20 x^{2}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$2 x \cdot \sqrt{20 x^{2}}$

Step 3

Rewrite $20 x^{2}$ as ${(2 x)}^{2} \cdot 5$ .

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Step 3.1

Factor $4$ out of $20$ .

$2 x \cdot \sqrt{4 (5) x^{2}}$

Step 3.2

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

$2 x \cdot \sqrt{2^{2} \cdot 5 x^{2}}$

Step 3.3

Move $5$ .

$2 x \cdot \sqrt{2^{2} x^{2} \cdot 5}$

Step 3.4

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

$2 x \cdot \sqrt{{(2 x)}^{2} \cdot 5}$

$2 x \cdot \sqrt{{(2 x)}^{2} \cdot 5}$

Step 4

Pull terms out from under the radical.

$2 x \cdot (2 x \sqrt{5})$

Step 5

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

$2 (x \cdot x) \cdot (2 \sqrt{5})$

Step 5.2

Multiply $x$ by $x$ .

$2 x^{2} \cdot (2 \sqrt{5})$

$2 x^{2} \cdot (2 \sqrt{5})$

Step 6

Multiply $2$ by $2$ .

$4 x^{2} \sqrt{5}$

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