Basic Math Examples

4 \sqrt{56 a^{14}}

$4 \sqrt{56 a^{14}}$

Step 1

Rewrite

56 a^{14}

$56 a^{14}$ as

{(2 a^{7})}^{2} \cdot 14

${(2 a^{7})}^{2} \cdot 14$ .

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Step 1.1

Factor

4

$4$ out of

56

$56$ .

4 \sqrt{4 (14) a^{14}}

$4 \sqrt{4 (14) a^{14}}$

Step 1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

4 \sqrt{2^{2} \cdot 14 a^{14}}

$4 \sqrt{2^{2} \cdot 14 a^{14}}$

Step 1.3

Rewrite

a^{14}

$a^{14}$ as

{(a^{7})}^{2}

${(a^{7})}^{2}$ .

4 \sqrt{2^{2} \cdot 14 {(a^{7})}^{2}}

$4 \sqrt{2^{2} \cdot 14 {(a^{7})}^{2}}$

Step 1.4

Move

14

$14$ .

4 \sqrt{2^{2} {(a^{7})}^{2} \cdot 14}

$4 \sqrt{2^{2} {(a^{7})}^{2} \cdot 14}$

Step 1.5

Rewrite

2^{2} {(a^{7})}^{2}

$2^{2} {(a^{7})}^{2}$ as

{(2 a^{7})}^{2}

${(2 a^{7})}^{2}$ .

4 \sqrt{{(2 a^{7})}^{2} \cdot 14}

$4 \sqrt{{(2 a^{7})}^{2} \cdot 14}$

4 \sqrt{{(2 a^{7})}^{2} \cdot 14}

$4 \sqrt{{(2 a^{7})}^{2} \cdot 14}$

Step 2

Pull terms out from under the radical.

4 (2 a^{7} \sqrt{14})

$4 (2 a^{7} \sqrt{14})$

Step 3

Multiply

2

$2$ by

4

$4$ .

8 a^{7} \sqrt{14}

$8 a^{7} \sqrt{14}$

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

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