Simplify square root of 9* square root of 5* square root of 2

$\sqrt{9} \cdot \sqrt{5} \cdot \sqrt{2}$

Step 1

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

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

Step 2

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

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

Step 3

Multiply $3 \sqrt{5} \sqrt{2}$ .

Combine using the product rule for radicals.

$3 \sqrt{2 \cdot 5}$

Multiply $2$ by $5$ .

$3 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{10}$

Decimal Form:

$9.48683298 \dots$