Pre-Algebra Examples

$\sqrt{16 x^{3}} \div \sqrt{8 x}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{16 x^{3}}}{\sqrt{8 x}}$

Step 2

Combine $\sqrt{16 x^{3}}$ and $\sqrt{8 x}$ into a single radical.

$\sqrt{\frac{16 x^{3}}{8 x}}$

Step 3

Reduce the expression $\frac{16 x^{3}}{8 x}$ by cancelling the common factors.

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Step 3.1

Factor $8$ out of $16 x^{3}$ .

$\sqrt{\frac{8 (2 x^{3})}{8 x}}$

Step 3.2

Factor $8$ out of $8 x$ .

$\sqrt{\frac{8 (2 x^{3})}{8 (x)}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{8 (2 x^{3})}{8 x}}$

Step 3.4

Rewrite the expression.

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

Step 4

Cancel the common factor of $x^{3}$ and $x$ .

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Step 4.1

Factor $x$ out of $2 x^{3}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Raise $x$ to the power of $1$ .

$\sqrt{\frac{x (2 x^{2})}{x^{1}}}$

Step 4.2.2

Factor $x$ out of $x^{1}$ .

$\sqrt{\frac{x (2 x^{2})}{x \cdot 1}}$

Step 4.2.3

Cancel the common factor.

$\sqrt{\frac{x (2 x^{2})}{x \cdot 1}}$

Step 4.2.4

Rewrite the expression.

$\sqrt{\frac{2 x^{2}}{1}}$

Step 4.2.5

Divide $2 x^{2}$ by $1$ .

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

$x \sqrt{2}$