Finite Math Examples

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

Step 1

Multiply $5$ by $4$ .

$- 2 \sqrt{20 \sqrt{2 - 3 \sqrt{3}}}$

Step 2

Rewrite $20 \sqrt{2 - 3 \sqrt{3}}$ as $2^{2} \cdot (5 \sqrt{2 - 3 \sqrt{3}})$ .

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Step 2.1

Factor $4$ out of $20$ .

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

Step 2.2

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

$- 2 \sqrt{2^{2} \cdot 5 \sqrt{2 - 3 \sqrt{3}}}$

Step 2.3

Add parentheses.

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

Step 3

Pull terms out from under the radical.

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

Step 4

Multiply $2$ by $- 2$ .

$- 4 \sqrt{5 \sqrt{2 - 3 \sqrt{3}}}$