Algebra Examples

\sqrt{48 x^{7}}

$\sqrt{48 x^{7}}$

Step 1

Rewrite

48 x^{7}

$48 x^{7}$ as

{(4 x^{3})}^{2} \cdot (3 x)

${(4 x^{3})}^{2} \cdot (3 x)$ .

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Step 1.1

Factor

16

$16$ out of

48

$48$ .

\sqrt{16 (3) x^{7}}

$\sqrt{16 (3) x^{7}}$

Step 1.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

\sqrt{4^{2} \cdot 3 x^{7}}

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

Step 1.3

Factor out

x^{6}

$x^{6}$ .

\sqrt{4^{2} \cdot 3 (x^{6} x)}

$\sqrt{4^{2} \cdot 3 (x^{6} x)}$

Step 1.4

Rewrite

x^{6}

$x^{6}$ as

{(x^{3})}^{2}

${(x^{3})}^{2}$ .

\sqrt{4^{2} \cdot 3 ({(x^{3})}^{2} x)}

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

Step 1.5

Move

3

$3$ .

\sqrt{4^{2} {(x^{3})}^{2} \cdot 3 x}

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

Step 1.6

Rewrite

4^{2} {(x^{3})}^{2}

$4^{2} {(x^{3})}^{2}$ as

{(4 x^{3})}^{2}

${(4 x^{3})}^{2}$ .

\sqrt{{(4 x^{3})}^{2} \cdot 3 x}

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

Step 1.7

Add parentheses.

\sqrt{{(4 x^{3})}^{2} \cdot (3 x)}

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

\sqrt{{(4 x^{3})}^{2} \cdot (3 x)}

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

Step 2

Pull terms out from under the radical.

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

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

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

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