Simplify the Radical Expression 3 square root of 3(4-3 square root of 5)

$3 \sqrt{3} (4 - 3 \sqrt{5})$

Apply the distributive property.

$3 \sqrt{3} \cdot 4 + 3 \sqrt{3} (- 3 \sqrt{5})$

Multiply $4$ by $3$ .

$12 \sqrt{3} + 3 \sqrt{3} (- 3 \sqrt{5})$

Multiply $3 \sqrt{3} (- 3 \sqrt{5})$ .

Multiply $- 3$ by $3$ .

$12 \sqrt{3} - 9 \sqrt{3} \sqrt{5}$

Combine using the product rule for radicals.

$12 \sqrt{3} - 9 \sqrt{5 \cdot 3}$

Multiply $5$ by $3$ .

$12 \sqrt{3} - 9 \sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{3} - 9 \sqrt{15}$

Decimal Form:

$- 14.07224042 \dots$