Simplify 2 square root of 7(3 square root of 12+5 square root of 8)

$2 \sqrt{7} (3 \sqrt{12} + 5 \sqrt{8})$

Simplify each term.

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$2 \sqrt{7} (3 \sqrt{4 (3)} + 5 \sqrt{8})$

Rewrite $4$ as $2^{2}$ .

$2 \sqrt{7} (3 \sqrt{2^{2} \cdot 3} + 5 \sqrt{8})$

Pull terms out from under the radical.

$2 \sqrt{7} (3 (2 \sqrt{3}) + 5 \sqrt{8})$

Multiply $2$ by $3$ .

$2 \sqrt{7} (6 \sqrt{3} + 5 \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$2 \sqrt{7} (6 \sqrt{3} + 5 \sqrt{4 (2)})$

Rewrite $4$ as $2^{2}$ .

$2 \sqrt{7} (6 \sqrt{3} + 5 \sqrt{2^{2} \cdot 2})$

Pull terms out from under the radical.

$2 \sqrt{7} (6 \sqrt{3} + 5 (2 \sqrt{2}))$

Multiply $2$ by $5$ .

$2 \sqrt{7} (6 \sqrt{3} + 10 \sqrt{2})$

Apply the distributive property.

$2 \sqrt{7} (6 \sqrt{3}) + 2 \sqrt{7} (10 \sqrt{2})$

Multiply $2 \sqrt{7} (6 \sqrt{3})$ .

Multiply $6$ by $2$ .

$12 \sqrt{7} \sqrt{3} + 2 \sqrt{7} (10 \sqrt{2})$

Combine using the product rule for radicals.

$12 \sqrt{3 \cdot 7} + 2 \sqrt{7} (10 \sqrt{2})$

Multiply $3$ by $7$ .

$12 \sqrt{21} + 2 \sqrt{7} (10 \sqrt{2})$

Multiply $2 \sqrt{7} (10 \sqrt{2})$ .

Multiply $10$ by $2$ .

$12 \sqrt{21} + 20 \sqrt{7} \sqrt{2}$

Combine using the product rule for radicals.

$12 \sqrt{21} + 20 \sqrt{2 \cdot 7}$

Multiply $2$ by $7$ .

$12 \sqrt{21} + 20 \sqrt{14}$

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{21} + 20 \sqrt{14}$

Decimal Form:

$129.82405607 \dots$