Basic Math Examples

$\sqrt{\frac{g^{3}}{7 g}}$

Step 1

Reduce the expression $\frac{g^{3}}{7 g}$ by cancelling the common factors.

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Step 1.1

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

$\sqrt{\frac{g \cdot g^{2}}{7 g}}$

Step 1.2

Factor $g$ out of $7 g$ .

$\sqrt{\frac{g \cdot g^{2}}{g \cdot 7}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{g \cdot g^{2}}{g \cdot 7}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{g^{2}}{7}}$

Step 2

Rewrite $\sqrt{\frac{g^{2}}{7}}$ as $\frac{\sqrt{g^{2}}}{\sqrt{7}}$ .

$\frac{\sqrt{g^{2}}}{\sqrt{7}}$

Step 3

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

$\frac{g}{\sqrt{7}}$

Step 4

Multiply $\frac{g}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{g}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{g}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{g \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Step 5.2

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{g \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Step 5.3

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{g \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

Step 5.4

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

$\frac{g \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

$\frac{g \sqrt{7}}{{\sqrt{7}}^{2}}$

Step 5.6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 5.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{g \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

Step 5.6.2

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

$\frac{g \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

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

$\frac{g \sqrt{7}}{7^{\frac{2}{2}}}$

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

$\frac{g \sqrt{7}}{7^{\frac{2}{2}}}$

Step 5.6.4.2

Rewrite the expression.

$\frac{g \sqrt{7}}{7^{1}}$

Step 5.6.5

Evaluate the exponent.

$\frac{g \sqrt{7}}{7}$