Simplify square root of 8* square root of 18*5 square root of 4

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

Step 1

Combine using the product rule for radicals.

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

Step 2

Write the expression using exponents.

Multiply $8$ by $18$ .

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

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

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

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

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

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 $12 (5 \cdot 2)$ .

Multiply $5$ by $2$ .

$12 \cdot 10$

Multiply $12$ by $10$ .

$120$