Linear Algebra Examples

$\frac{13.05}{\sqrt{90}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 1.1.1

Factor $9$ out of $90$ .

$\frac{13.05}{\sqrt{9 (10)}}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{13.05}{\sqrt{3^{2} \cdot 10}}$

Step 1.2

Pull terms out from under the radical.

$\frac{13.05}{3 \sqrt{10}}$

Step 2

Multiply $\frac{13.05}{3 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{13.05}{3 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{13.05}{3 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{13.05 \sqrt{10}}{3 \sqrt{10} \sqrt{10}}$

Step 3.2

Move $\sqrt{10}$ .

$\frac{13.05 \sqrt{10}}{3 (\sqrt{10} \sqrt{10})}$

Step 3.3

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{13.05 \sqrt{10}}{3 ({\sqrt{10}}^{1} \sqrt{10})}$

Step 3.4

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{13.05 \sqrt{10}}{3 ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

Step 3.5

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

$\frac{13.05 \sqrt{10}}{3 {\sqrt{10}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{13.05 \sqrt{10}}{3 {\sqrt{10}}^{2}}$

Step 3.7

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{13.05 \sqrt{10}}{3 {(10^{\frac{1}{2}})}^{2}}$

Step 3.7.2

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

$\frac{13.05 \sqrt{10}}{3 \cdot 10^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

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

$\frac{13.05 \sqrt{10}}{3 \cdot 10^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

$\frac{13.05 \sqrt{10}}{3 \cdot 10^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\frac{13.05 \sqrt{10}}{3 \cdot 10^{1}}$

Step 3.7.5

Evaluate the exponent.

$\frac{13.05 \sqrt{10}}{3 \cdot 10}$

Step 4

Multiply $13.05$ by $\sqrt{10}$ .

$\frac{41.26772346}{3 \cdot 10}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $3$ by $10$ .

$\frac{41.26772346}{30}$

Step 5.2

Divide $41.26772346$ by $30$ .

$1.37559078$