Algebra Examples

$\sqrt{8} \cdot \sqrt{18} \cdot 5 \sqrt{4}$

Step 1

Combine using the product rule for radicals.

$\sqrt{8 \cdot 18} \cdot (5 \sqrt{4})$

Step 2

Write the expression using exponents.

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Step 2.1

Multiply $8$ by $18$ .

$\sqrt{144} \cdot (5 \sqrt{4})$

Step 2.2

Rewrite $144$ as $12^{2}$ .

$\sqrt{12^{2}} \cdot (5 \sqrt{4})$

Step 2.3

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

$12 \cdot (5 \sqrt{4})$

Step 2.4

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

$12 \cdot (5 \sqrt{2^{2}})$

Step 3

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

$12 \cdot (5 \cdot 2)$

Step 4

Multiply $12 (5 \cdot 2)$ .

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Step 4.1

Multiply $5$ by $2$ .

$12 \cdot 10$

Step 4.2

Multiply $12$ by $10$ .

$120$