Simplify 10 square root of 10*4 square root of 12

$10 \sqrt{10} \cdot 4 \sqrt{12}$

Step 1

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

Factor $4$ out of $12$ .

$10 \sqrt{10} \cdot (4 \sqrt{4 (3)})$

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

$10 \sqrt{10} \cdot (4 \sqrt{2^{2} \cdot 3})$

$10 \sqrt{10} \cdot (4 \sqrt{2^{2} \cdot 3})$

Step 2

Pull terms out from under the radical.

$10 \sqrt{10} \cdot (4 (2 \sqrt{3}))$

Step 3

Multiply $2$ by $4$ .

$10 \sqrt{10} \cdot (8 \sqrt{3})$

Step 4

Multiply $10 \sqrt{10} (8 \sqrt{3})$ .

Multiply $8$ by $10$ .

$80 \sqrt{10} \sqrt{3}$

Combine using the product rule for radicals.

$80 \sqrt{3 \cdot 10}$

Multiply $3$ by $10$ .

$80 \sqrt{30}$

$80 \sqrt{30}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$80 \sqrt{30}$

Decimal Form:

$438.17804600 \dots$

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