Basic Math Examples

\sqrt{64 x^{5}}

$\sqrt{64 x^{5}}$

Step 1

Rewrite

64 x^{5}

$64 x^{5}$ as

{(8 x^{2})}^{2} x

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

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Step 1.1

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

\sqrt{8^{2} x^{5}}

$\sqrt{8^{2} x^{5}}$

Step 1.2

Factor out

x^{4}

$x^{4}$ .

\sqrt{8^{2} (x^{4} x)}

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

Step 1.3

Rewrite

x^{4}

$x^{4}$ as

{(x^{2})}^{2}

${(x^{2})}^{2}$ .

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

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

Step 1.4

Rewrite

8^{2} {(x^{2})}^{2}

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

{(8 x^{2})}^{2}

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

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

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

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

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

Step 2

Pull terms out from under the radical.

8 x^{2} \sqrt{x}

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

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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