Basic Math Examples

$\sqrt{\frac{63}{18 x}}$

Step 1

Reduce the expression $\frac{63}{18 x}$ by cancelling the common factors.

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Step 1.1

Factor $9$ out of $63$ .

$\sqrt{\frac{9 (7)}{18 x}}$

Step 1.2

Factor $9$ out of $18 x$ .

$\sqrt{\frac{9 (7)}{9 (2 x)}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{9 \cdot 7}{9 (2 x)}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{7}{2 x}}$

Step 2

Rewrite $\sqrt{\frac{7}{2 x}}$ as $\frac{\sqrt{7}}{\sqrt{2 x}}$ .

$\frac{\sqrt{7}}{\sqrt{2 x}}$

Step 3

Multiply $\frac{\sqrt{7}}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{\sqrt{7}}{\sqrt{2 x}} \cdot \frac{\sqrt{2 x}}{\sqrt{2 x}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{\sqrt{7}}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{\sqrt{7} \sqrt{2 x}}{\sqrt{2 x} \sqrt{2 x}}$

Step 4.2

Raise $\sqrt{2 x}$ to the power of $1$ .

$\frac{\sqrt{7} \sqrt{2 x}}{{\sqrt{2 x}}^{1} \sqrt{2 x}}$

Step 4.3

Raise $\sqrt{2 x}$ to the power of $1$ .

$\frac{\sqrt{7} \sqrt{2 x}}{{\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1}}$

Step 4.4

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

$\frac{\sqrt{7} \sqrt{2 x}}{{\sqrt{2 x}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

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

Step 4.6

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

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Step 4.6.1

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

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

Step 4.6.2

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

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

Step 4.6.3

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

$\frac{\sqrt{7} \sqrt{2 x}}{{(2 x)}^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt{7} \sqrt{2 x}}{{(2 x)}^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

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

Step 4.6.5

Simplify.

$\frac{\sqrt{7} \sqrt{2 x}}{2 x}$

Step 5

Simplify the numerator.

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Step 5.1

Combine using the product rule for radicals.

$\frac{\sqrt{7 (2 x)}}{2 x}$

Step 5.2

Multiply $7$ by $2$ .

$\frac{\sqrt{14 x}}{2 x}$