Algebra Examples

$- 4 \sqrt{28 x} + \sqrt{7 x^{3}}$

Step 1

Rewrite $28 x$ as $2^{2} \cdot (7 x)$ .

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Step 1.1

Factor $4$ out of $28$ .

$- 4 \sqrt{4 (7) x} + \sqrt{7 x^{3}}$

Step 1.2

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

$- 4 \sqrt{2^{2} \cdot 7 x} + \sqrt{7 x^{3}}$

Step 1.3

Add parentheses.

$- 4 \sqrt{2^{2} \cdot (7 x)} + \sqrt{7 x^{3}}$

$- 4 \sqrt{2^{2} \cdot (7 x)} + \sqrt{7 x^{3}}$

Step 2

Pull terms out from under the radical.

$- 4 (2 \sqrt{7 x}) + \sqrt{7 x^{3}}$

Step 3

Multiply $2$ by $- 4$ .

$- 8 \sqrt{7 x} + \sqrt{7 x^{3}}$

Step 4

Rewrite $7 x^{3}$ as $x^{2} \cdot (7 x)$ .

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Step 4.1

Factor out $x^{2}$ .

$- 8 \sqrt{7 x} + \sqrt{7 (x^{2} x)}$

Step 4.2

Reorder $7$ and $x^{2}$ .

$- 8 \sqrt{7 x} + \sqrt{x^{2} \cdot 7 x}$

Step 4.3

Add parentheses.

$- 8 \sqrt{7 x} + \sqrt{x^{2} \cdot (7 x)}$

$- 8 \sqrt{7 x} + \sqrt{x^{2} \cdot (7 x)}$

Step 5

Pull terms out from under the radical.

$- 8 \sqrt{7 x} + x \sqrt{7 x}$

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