Finite Math Examples

$\sqrt{16 - 4 r^{2}}$

Step 1

Factor $4$ out of $16 - 4 r^{2}$ .

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Step 1.1

Factor $4$ out of $16$ .

$\sqrt{4 (4) - 4 r^{2}}$

Step 1.2

Factor $4$ out of $- 4 r^{2}$ .

$\sqrt{4 (4) + 4 (- r^{2})}$

Step 1.3

Factor $4$ out of $4 (4) + 4 (- r^{2})$ .

$\sqrt{4 (4 - r^{2})}$

Step 2

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

$\sqrt{4 (2^{2} - r^{2})}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = r$ .

$\sqrt{4 (2 + r) (2 - r)}$

Step 4

Rewrite $4 (2 + r) (2 - r)$ as $2^{2} ((2 + r) (2 - r))$ .

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Step 4.1

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

$\sqrt{2^{2} (2 + r) (2 - r)}$

Step 4.2

Add parentheses.

$\sqrt{2^{2} ((2 + r) (2 - r))}$

Step 5

Pull terms out from under the radical.

$2 \sqrt{(2 + r) (2 - r)}$