Evaluate (4 square root of 12)(3 square root of 20)

$(4 \sqrt{12}) (3 \sqrt{20})$

Step 1

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

Factor $4$ out of $12$ .

$4 \sqrt{4 (3)} (3 \sqrt{20})$

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

$4 \sqrt{2^{2} \cdot 3} (3 \sqrt{20})$

$4 \sqrt{2^{2} \cdot 3} (3 \sqrt{20})$

Step 2

Pull terms out from under the radical.

$4 (2 \sqrt{3}) (3 \sqrt{20})$

Step 3

Multiply $2$ by $4$ .

$8 \sqrt{3} (3 \sqrt{20})$

Step 4

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$8 \sqrt{3} (3 \sqrt{4 (5)})$

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

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $2$ by $3$ .

$8 \sqrt{3} (6 \sqrt{5})$

Step 7

Multiply $8 \sqrt{3} (6 \sqrt{5})$ .

Multiply $6$ by $8$ .

$48 \sqrt{3} \sqrt{5}$

Combine using the product rule for radicals.

$48 \sqrt{5 \cdot 3}$

Multiply $5$ by $3$ .

$48 \sqrt{15}$

$48 \sqrt{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$48 \sqrt{15}$

Decimal Form:

$185.90320061 \dots$

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