Linear Algebra Examples

$\frac{\sqrt{14 - 3}}{\sqrt{14 + 3}}$

Step 1

Subtract $3$ from $14$ .

$\frac{\sqrt{11}}{\sqrt{14 + 3}}$

Step 2

Add $14$ and $3$ .

$\frac{\sqrt{11}}{\sqrt{17}}$

Step 3

Multiply $\frac{\sqrt{11}}{\sqrt{17}}$ by $\frac{\sqrt{17}}{\sqrt{17}}$ .

$\frac{\sqrt{11}}{\sqrt{17}} \cdot \frac{\sqrt{17}}{\sqrt{17}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{\sqrt{11}}{\sqrt{17}}$ by $\frac{\sqrt{17}}{\sqrt{17}}$ .

$\frac{\sqrt{11} \sqrt{17}}{\sqrt{17} \sqrt{17}}$

Step 4.2

Raise $\sqrt{17}$ to the power of $1$ .

$\frac{\sqrt{11} \sqrt{17}}{{\sqrt{17}}^{1} \sqrt{17}}$

Step 4.3

Raise $\sqrt{17}$ to the power of $1$ .

$\frac{\sqrt{11} \sqrt{17}}{{\sqrt{17}}^{1} {\sqrt{17}}^{1}}$

Step 4.4

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

$\frac{\sqrt{11} \sqrt{17}}{{\sqrt{17}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{\sqrt{11} \sqrt{17}}{{\sqrt{17}}^{2}}$

Step 4.6

Rewrite ${\sqrt{17}}^{2}$ as $17$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$\frac{\sqrt{11} \sqrt{17}}{{(17^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$\frac{\sqrt{11} \sqrt{17}}{17^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$\frac{\sqrt{11} \sqrt{17}}{17^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt{11} \sqrt{17}}{17^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{\sqrt{11} \sqrt{17}}{17^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{\sqrt{11} \sqrt{17}}{17}$

Step 5

Simplify the numerator.

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Step 5.1

Combine using the product rule for radicals.

$\frac{\sqrt{11 \cdot 17}}{17}$

Step 5.2

Multiply $11$ by $17$ .

$\frac{\sqrt{187}}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{187}}{17}$

Decimal Form:

$0.80439966 \dots$