Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

Tap for more steps...

Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

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

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

Step 1.1.3

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $2$ by $- 1$ .

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

Step 2

Add $\sqrt{2 x}$ and $2 \sqrt{2 x}$ .

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