Simplify ( square root of 45* square root of 20)/2

$\frac{\sqrt{45} \cdot \sqrt{20}}{2}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{45 \cdot 20}}{2}$

Multiply $45$ by $20$ .

$\frac{\sqrt{900}}{2}$

Simplify the numerator.

Rewrite $900$ as $30^{2}$ .

$\frac{\sqrt{30^{2}}}{2}$

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

$\frac{30}{2}$

Divide $30$ by $2$ .

$15$