Linear Algebra Examples

$\frac{65160}{\sqrt{71.87} x \sqrt{923.25}}$

Step 1

Simplify the denominator.

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Step 1.1

Combine using the product rule for radicals.

$\frac{65160}{x \sqrt{71.87 \cdot 923.25}}$

Step 1.2

Multiply $71.87$ by $923.25$ .

$\frac{65160}{x \sqrt{66353.9775}}$

Step 2

Multiply $\frac{65160}{x \sqrt{66353.9775}}$ by $\frac{\sqrt{66353.9775}}{\sqrt{66353.9775}}$ .

$\frac{65160}{x \sqrt{66353.9775}} \cdot \frac{\sqrt{66353.9775}}{\sqrt{66353.9775}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{65160}{x \sqrt{66353.9775}}$ by $\frac{\sqrt{66353.9775}}{\sqrt{66353.9775}}$ .

$\frac{65160 \sqrt{66353.9775}}{x \sqrt{66353.9775} \sqrt{66353.9775}}$

Step 3.2

Move $\sqrt{66353.9775}$ .

$\frac{65160 \sqrt{66353.9775}}{x (\sqrt{66353.9775} \sqrt{66353.9775})}$

Step 3.3

Raise $\sqrt{66353.9775}$ to the power of $1$ .

$\frac{65160 \sqrt{66353.9775}}{x ({\sqrt{66353.9775}}^{1} \sqrt{66353.9775})}$

Step 3.4

Raise $\sqrt{66353.9775}$ to the power of $1$ .

$\frac{65160 \sqrt{66353.9775}}{x ({\sqrt{66353.9775}}^{1} {\sqrt{66353.9775}}^{1})}$

Step 3.5

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

$\frac{65160 \sqrt{66353.9775}}{x {\sqrt{66353.9775}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{65160 \sqrt{66353.9775}}{x {\sqrt{66353.9775}}^{2}}$

Step 3.7

Rewrite ${\sqrt{66353.9775}}^{2}$ as $66353.9775$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{66353.9775}$ as ${66353.9775}^{\frac{1}{2}}$ .

$\frac{65160 \sqrt{66353.9775}}{x {({66353.9775}^{\frac{1}{2}})}^{2}}$

Step 3.7.2

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

$\frac{65160 \sqrt{66353.9775}}{x \cdot {66353.9775}^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

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

$\frac{65160 \sqrt{66353.9775}}{x \cdot {66353.9775}^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

$\frac{65160 \sqrt{66353.9775}}{x \cdot {66353.9775}^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\frac{65160 \sqrt{66353.9775}}{x \cdot {66353.9775}^{1}}$

Step 3.7.5

Evaluate the exponent.

$\frac{65160 \sqrt{66353.9775}}{x \cdot 66353.9775}$

Step 4

Move $66353.9775$ to the left of $x$ .

$\frac{65160 \sqrt{66353.9775}}{66353.9775 \cdot x}$

Step 5

Factor $65160 \sqrt{66353.9775}$ out of $65160 \sqrt{66353.9775}$ .

$\frac{65160 \sqrt{66353.9775} (1)}{66353.9775 \cdot x}$

Step 6

Factor $66353.9775$ out of $66353.9775 \cdot x$ .

$\frac{65160 \sqrt{66353.9775} (1)}{66353.9775 (x)}$

Step 7

Separate fractions.

$\frac{65160 \sqrt{66353.9775}}{66353.9775} \cdot \frac{1}{x}$

Step 8

Evaluate the root.

$\frac{65160 \cdot 257.59265808}{66353.9775} \cdot \frac{1}{x}$

Step 9

Simplify the expression.

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Step 9.1

Multiply $65160$ by $257.59265808$ .

$\frac{16784737.60090767}{66353.9775} \cdot \frac{1}{x}$

Step 9.2

Divide $16784737.60090767$ by $66353.9775$ .

$252.95752015 \frac{1}{x}$

Step 10

Combine $252.95752015$ and $\frac{1}{x}$ .

$\frac{252.95752015}{x}$