Algebra Examples

$\sqrt{32 x} + 4 \sqrt{8 x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $32 x$ as ${(2^{2})}^{2} \cdot (2 x)$ .

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Step 1.1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) x} + 4 \sqrt{8 x}$

Step 1.1.2

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

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

Step 1.1.3

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

$\sqrt{{(2^{2})}^{2} \cdot 2 x} + 4 \sqrt{8 x}$

Step 1.1.4

Add parentheses.

$\sqrt{{(2^{2})}^{2} \cdot (2 x)} + 4 \sqrt{8 x}$

$\sqrt{{(2^{2})}^{2} \cdot (2 x)} + 4 \sqrt{8 x}$

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Raise $2$ to the power of $2$ .

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

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $8$ .

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

Step 1.4.2

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

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

Step 1.4.3

Add parentheses.

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

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $2$ by $4$ .

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

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

Step 2

Add $4 \sqrt{2 x}$ and $8 \sqrt{2 x}$ .

$12 \sqrt{2 x}$

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