Basic Math Examples

$\sqrt{16 m^{3}} \div \sqrt{2 m}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{16 m^{3}}}{\sqrt{2 m}}$

Step 2

Combine $\sqrt{16 m^{3}}$ and $\sqrt{2 m}$ into a single radical.

$\sqrt{\frac{16 m^{3}}{2 m}}$

Step 3

Reduce the expression $\frac{16 m^{3}}{2 m}$ by cancelling the common factors.

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Step 3.1

Factor $2$ out of $16 m^{3}$ .

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

Step 3.2

Factor $2$ out of $2 m$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

$\sqrt{\frac{8 m^{3}}{m}}$

Step 4

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

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Step 4.1

Factor $m$ out of $8 m^{3}$ .

$\sqrt{\frac{m (8 m^{2})}{m}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\sqrt{\frac{m (8 m^{2})}{m^{1}}}$

Step 4.2.2

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

$\sqrt{\frac{m (8 m^{2})}{m \cdot 1}}$

Step 4.2.3

Cancel the common factor.

$\sqrt{\frac{m (8 m^{2})}{m \cdot 1}}$

Step 4.2.4

Rewrite the expression.

$\sqrt{\frac{8 m^{2}}{1}}$

Step 4.2.5

Divide $8 m^{2}$ by $1$ .

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

Step 5

Rewrite $8 m^{2}$ as ${(2 m)}^{2} \cdot 2$ .

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Step 5.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) m^{2}}$

Step 5.2

Rewrite $4$ as $2^{2}$ .

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

Step 5.3

Move $2$ .

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

Step 5.4

Rewrite $2^{2} m^{2}$ as ${(2 m)}^{2}$ .

$\sqrt{{(2 m)}^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$2 m \sqrt{2}$