Simplify 2 square root of 5(3 square root of 3+6 square root of 2)x^3

$2 \sqrt{5} (3 \sqrt{3} + 6 \sqrt{2}) x^{3}$

Step 1

Apply the distributive property.

$(2 \sqrt{5} (3 \sqrt{3}) + 2 \sqrt{5} (6 \sqrt{2})) x^{3}$

Step 2

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

Multiply $3$ by $2$ .

$(6 \sqrt{5} \sqrt{3} + 2 \sqrt{5} (6 \sqrt{2})) x^{3}$

Combine using the product rule for radicals.

$(6 \sqrt{3 \cdot 5} + 2 \sqrt{5} (6 \sqrt{2})) x^{3}$

Multiply $3$ by $5$ .

$(6 \sqrt{15} + 2 \sqrt{5} (6 \sqrt{2})) x^{3}$

Step 3

Multiply $2 \sqrt{5} (6 \sqrt{2})$ .

Multiply $6$ by $2$ .

$(6 \sqrt{15} + 12 \sqrt{5} \sqrt{2}) x^{3}$

Combine using the product rule for radicals.

$(6 \sqrt{15} + 12 \sqrt{2 \cdot 5}) x^{3}$

Multiply $2$ by $5$ .

$(6 \sqrt{15} + 12 \sqrt{10}) x^{3}$

Step 4

Apply the distributive property.

$6 \sqrt{15} x^{3} + 12 \sqrt{10} x^{3}$