Basic Math Examples

$4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{8}})$

Step 1

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

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Step 1.1

Factor $4$ out of $8$ .

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

Step 1.2

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

$4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{2^{2} \cdot 2}})$

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $- 3$ .

$4 \sqrt{2} (5 \sqrt{6 - 6 \sqrt{2}})$

Step 4

Multiply $4 \sqrt{2} (5 \sqrt{6 - 6 \sqrt{2}})$ .

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Step 4.1

Multiply $5$ by $4$ .

$20 \sqrt{2} \sqrt{6 - 6 \sqrt{2}}$

Step 4.2

Combine using the product rule for radicals.

$20 \sqrt{(6 - 6 \sqrt{2}) \cdot 2}$