Finite Math Examples

$\sqrt{2 x} (\sqrt{8 x - \sqrt{32}})$

Step 1

Rewrite $32$ as $4^{2} \cdot 2$ .

Tap for more steps...

Step 1.1

Factor $16$ out of $32$ .

$\sqrt{2 x} \sqrt{8 x - \sqrt{16 (2)}}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{2 x} \sqrt{8 x - \sqrt{4^{2} \cdot 2}}$

$\sqrt{2 x} \sqrt{8 x - \sqrt{4^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

$\sqrt{2 x} \sqrt{8 x - (4 \sqrt{2})}$

Step 3

Multiply $4$ by $- 1$ .

$\sqrt{2 x} \sqrt{8 x - 4 \sqrt{2}}$

Step 4

Factor $4$ out of $8 x - 4 \sqrt{2}$ .

Tap for more steps...

Step 4.1

Factor $4$ out of $8 x$ .

$\sqrt{2 x} \sqrt{4 (2 x) - 4 \sqrt{2}}$

Step 4.2

Factor $4$ out of $- 4 \sqrt{2}$ .

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

Step 4.3

Factor $4$ out of $4 (2 x) + 4 (- \sqrt{2})$ .

$\sqrt{2 x} \sqrt{4 (2 x - \sqrt{2})}$

$\sqrt{2 x} \sqrt{4 (2 x - \sqrt{2})}$

Step 5

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

$\sqrt{2 x} \sqrt{2^{2} (2 x - \sqrt{2})}$

Step 6

Pull terms out from under the radical.

$\sqrt{2 x} (2 \sqrt{2 x - \sqrt{2}})$

Step 7

Rewrite using the commutative property of multiplication.

$2 \sqrt{2 x} \sqrt{2 x - \sqrt{2}}$

Step 8

Combine using the product rule for radicals.

$2 \sqrt{(2 x - \sqrt{2}) \cdot 2 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$