Algebra Examples

$5 \sqrt{20} \cdot 3 \sqrt{8}$

Step 1

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

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Step 1.1

Factor $4$ out of $20$ .

$5 \sqrt{4 (5)} \cdot 3 \sqrt{8}$

Step 1.2

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

$5 \sqrt{2^{2} \cdot 5} \cdot 3 \sqrt{8}$

Step 2

Pull terms out from under the radical.

$5 (| 2 | \sqrt{5}) \cdot 3 \sqrt{8}$

Step 3

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

$5 (2 \sqrt{5}) \cdot 3 \sqrt{8}$

Step 4

Multiply $2$ by $5$ .

$10 \sqrt{5} \cdot 3 \sqrt{8}$

Step 5

Multiply $3$ by $10$ .

$30 \sqrt{5} \sqrt{8}$

Step 6

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 6.1

Factor $4$ out of $8$ .

$30 \sqrt{5} \sqrt{4 (2)}$

Step 6.2

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

$30 \sqrt{5} \sqrt{2^{2} \cdot 2}$

Step 7

Pull terms out from under the radical.

$30 \sqrt{5} (| 2 | \sqrt{2})$

Step 8

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

$30 \sqrt{5} (2 \sqrt{2})$

Step 9

Multiply $30 \sqrt{5} (2 \sqrt{2})$ .

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Step 9.1

Multiply $2$ by $30$ .

$60 \sqrt{5} \sqrt{2}$

Step 9.2

Combine using the product rule for radicals.

$60 \sqrt{2 \cdot 5}$

Step 9.3

Multiply $2$ by $5$ .

$60 \sqrt{10}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$60 \sqrt{10}$

Decimal Form:

$189.73665961 \dots$