Algebra Examples

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

Step 1

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

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Step 1.1

Factor $4$ out of $20$ .

$\sqrt{4 (5) x^{2}} \cdot \sqrt{20 x}$

Step 1.2

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

$\sqrt{2^{2} \cdot 5 x^{2}} \cdot \sqrt{20 x}$

Step 1.3

Move $5$ .

$\sqrt{2^{2} x^{2} \cdot 5} \cdot \sqrt{20 x}$

Step 1.4

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

$\sqrt{{(2 x)}^{2} \cdot 5} \cdot \sqrt{20 x}$

Step 2

Pull terms out from under the radical.

$| 2 x | \sqrt{5} \cdot \sqrt{20 x}$

Step 3

Remove non-negative terms from the absolute value.

$2 | x | \sqrt{5} \cdot \sqrt{20 x}$

Step 4

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

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Step 4.1

Factor $4$ out of $20$ .

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

Step 4.2

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

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

Step 4.3

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 7

Multiply $2 | x | \sqrt{5} (2 \sqrt{5 x})$ .

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Step 7.1

Multiply $2$ by $2$ .

$4 | x | \sqrt{5} \sqrt{5 x}$

Step 7.2

Combine using the product rule for radicals.

$4 | x | \sqrt{5 x \cdot 5}$

Step 7.3

Multiply $5$ by $5$ .

$4 | x | \sqrt{25 x}$

Step 8

Rewrite $25$ as $5^{2}$ .

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

Step 9

Pull terms out from under the radical.

$4 | x | (| 5 | \sqrt{x})$

Step 10

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$4 | x | (5 \sqrt{x})$

Step 11

Multiply $5$ by $4$ .

$20 | x | \sqrt{x}$