Algebra Examples

$\sqrt{3} \cdot 2 \sqrt{2} \cdot 5 \sqrt{8} \cdot \sqrt{18}$

Step 1

Multiply $\sqrt{3} (2 \sqrt{2})$ .

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Step 1.1

Combine using the product rule for radicals.

$2 \sqrt{3 \cdot 2} \cdot (5 \sqrt{8}) \cdot \sqrt{18}$

Step 1.2

Multiply $3$ by $2$ .

$2 \sqrt{6} \cdot (5 \sqrt{8}) \cdot \sqrt{18}$

Step 2

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

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Step 2.1

Factor $4$ out of $8$ .

$2 \sqrt{6} \cdot (5 \sqrt{4 (2)}) \cdot \sqrt{18}$

Step 2.2

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

$2 \sqrt{6} \cdot (5 \sqrt{2^{2} \cdot 2}) \cdot \sqrt{18}$

Step 3

Pull terms out from under the radical.

$2 \sqrt{6} \cdot (5 (2 \sqrt{2})) \cdot \sqrt{18}$

Step 4

Multiply $2$ by $5$ .

$2 \sqrt{6} \cdot (10 \sqrt{2}) \cdot \sqrt{18}$

Step 5

Multiply $2 \sqrt{6} (10 \sqrt{2})$ .

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Step 5.1

Multiply $10$ by $2$ .

$20 \sqrt{6} \sqrt{2} \cdot \sqrt{18}$

Step 5.2

Combine using the product rule for radicals.

$20 \sqrt{2 \cdot 6} \cdot \sqrt{18}$

Step 5.3

Multiply $2$ by $6$ .

$20 \sqrt{12} \cdot \sqrt{18}$

Step 6

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 6.1

Factor $4$ out of $12$ .

$20 \sqrt{4 (3)} \cdot \sqrt{18}$

Step 6.2

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

$20 \sqrt{2^{2} \cdot 3} \cdot \sqrt{18}$

Step 7

Pull terms out from under the radical.

$20 (2 \sqrt{3}) \cdot \sqrt{18}$

Step 8

Multiply $2$ by $20$ .

$40 \sqrt{3} \cdot \sqrt{18}$

Step 9

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 9.1

Factor $9$ out of $18$ .

$40 \sqrt{3} \cdot \sqrt{9 (2)}$

Step 9.2

Rewrite $9$ as $3^{2}$ .

$40 \sqrt{3} \cdot \sqrt{3^{2} \cdot 2}$

Step 10

Pull terms out from under the radical.

$40 \sqrt{3} \cdot (3 \sqrt{2})$

Step 11

Multiply $40 \sqrt{3} (3 \sqrt{2})$ .

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Step 11.1

Multiply $3$ by $40$ .

$120 \sqrt{3} \sqrt{2}$

Step 11.2

Combine using the product rule for radicals.

$120 \sqrt{2 \cdot 3}$

Step 11.3

Multiply $2$ by $3$ .

$120 \sqrt{6}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$120 \sqrt{6}$

Decimal Form:

$293.93876913 \dots$