Algebra Examples

$\sqrt{{(4 x)}^{3}}$

Step 1

Apply the product rule to $4 x$ .

$\sqrt{4^{3} x^{3}}$

Step 2

Raise $4$ to the power of $3$ .

$\sqrt{64 x^{3}}$

Step 3

Rewrite $64 x^{3}$ as ${(8 x)}^{2} x$ .

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Step 3.1

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} x^{3}}$

Step 3.2

Factor out $x^{2}$ .

$\sqrt{8^{2} (x^{2} x)}$

Step 3.3

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

$\sqrt{{(8 x)}^{2} x}$

$\sqrt{{(8 x)}^{2} x}$

Step 4

Pull terms out from under the radical.

$8 x \sqrt{x}$

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