Simplify 2 square root of 3(4 square root of 5+ square root of 6)

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $2 \sqrt{3} (4 \sqrt{5})$ .

Multiply $4$ by $2$ .

$8 \sqrt{3} \sqrt{5} + 2 \sqrt{3} \sqrt{6}$

Combine using the product rule for radicals.

$8 \sqrt{5 \cdot 3} + 2 \sqrt{3} \sqrt{6}$

Multiply $5$ by $3$ .

$8 \sqrt{15} + 2 \sqrt{3} \sqrt{6}$

$8 \sqrt{15} + 2 \sqrt{3} \sqrt{6}$

Step 3

Multiply $2 \sqrt{3} \sqrt{6}$ .

Combine using the product rule for radicals.

$8 \sqrt{15} + 2 \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$8 \sqrt{15} + 2 \sqrt{18}$

$8 \sqrt{15} + 2 \sqrt{18}$

Step 4

Simplify each term.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$8 \sqrt{15} + 2 \sqrt{9 (2)}$

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

$8 \sqrt{15} + 2 \sqrt{3^{2} \cdot 2}$

$8 \sqrt{15} + 2 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$8 \sqrt{15} + 2 (3 \sqrt{2})$

Multiply $3$ by $2$ .

$8 \sqrt{15} + 6 \sqrt{2}$

$8 \sqrt{15} + 6 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{15} + 6 \sqrt{2}$

Decimal Form:

$39.46914814 \dots$

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