Algebra Examples

$\sqrt{\frac{48 m^{2}}{3 m^{3}}}$

Step 1

Reduce the expression $\frac{48 m^{2}}{3 m^{3}}$ by cancelling the common factors.

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Step 1.1

Factor $3$ out of $48 m^{2}$ .

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

Step 1.2

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

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

Cancel the common factor of $m^{2}$ and $m^{3}$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{16}{m}}$

Step 3

Rewrite $\sqrt{\frac{16}{m}}$ as $\frac{\sqrt{16}}{\sqrt{m}}$ .

$\frac{\sqrt{16}}{\sqrt{m}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}}}{\sqrt{m}}$

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4}{\sqrt{m}}$

Step 5

Multiply $\frac{4}{\sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

$\frac{4}{\sqrt{m}} \cdot \frac{\sqrt{m}}{\sqrt{m}}$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{4}{\sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

$\frac{4 \sqrt{m}}{\sqrt{m} \sqrt{m}}$

Step 6.2

Raise $\sqrt{m}$ to the power of $1$ .

$\frac{4 \sqrt{m}}{{\sqrt{m}}^{1} \sqrt{m}}$

Step 6.3

Raise $\sqrt{m}$ to the power of $1$ .

$\frac{4 \sqrt{m}}{{\sqrt{m}}^{1} {\sqrt{m}}^{1}}$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 \sqrt{m}}{{\sqrt{m}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$\frac{4 \sqrt{m}}{{\sqrt{m}}^{2}}$

Step 6.6

Rewrite ${\sqrt{m}}^{2}$ as $m$ .

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Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{m}$ as $m^{\frac{1}{2}}$ .

$\frac{4 \sqrt{m}}{{(m^{\frac{1}{2}})}^{2}}$

Step 6.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4 \sqrt{m}}{m^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{4 \sqrt{m}}{m^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$\frac{4 \sqrt{m}}{m^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$\frac{4 \sqrt{m}}{m^{1}}$

Step 6.6.5

Simplify.

$\frac{4 \sqrt{m}}{m}$