Finite Math Examples

$\sqrt{\frac{5}{3}} + {(\frac{14}{9})}^{2}$

Step 1

Write $\sqrt{\frac{5}{3}} + {(\frac{14}{9})}^{2}$ as a function.

$f (x) = \sqrt{\frac{5}{3}} + {(\frac{14}{9})}^{2}$

Step 2

Identify the degree of the function.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite $\sqrt{\frac{5}{3}}$ as $\frac{\sqrt{5}}{\sqrt{3}}$ .

$\frac{\sqrt{5}}{\sqrt{3}} + {(\frac{14}{9})}^{2}$

Step 2.1.2

Multiply $\frac{\sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt{5}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} + {(\frac{14}{9})}^{2}$

Step 2.1.3

Combine and simplify the denominator.

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Step 2.1.3.1

Multiply $\frac{\sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt{5} \sqrt{3}}{\sqrt{3} \sqrt{3}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.2

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.3

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.4

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

$\frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1 + 1}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.5

Add $1$ and $1$ .

$\frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{2}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 2.1.3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{\sqrt{5} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.6.2

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

$\frac{\sqrt{5} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.6.3

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

$\frac{\sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.6.4

Cancel the common factor of $2$ .

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Step 2.1.3.6.4.1

Cancel the common factor.

$\frac{\sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.6.4.2

Rewrite the expression.

$\frac{\sqrt{5} \sqrt{3}}{3^{1}} + {(\frac{14}{9})}^{2}$

Step 2.1.3.6.5

Evaluate the exponent.

$\frac{\sqrt{5} \sqrt{3}}{3} + {(\frac{14}{9})}^{2}$

Step 2.1.4

Simplify the numerator.

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Step 2.1.4.1

Combine using the product rule for radicals.

$\frac{\sqrt{5 \cdot 3}}{3} + {(\frac{14}{9})}^{2}$

Step 2.1.4.2

Multiply $5$ by $3$ .

$\frac{\sqrt{15}}{3} + {(\frac{14}{9})}^{2}$

Step 2.1.5

Apply the product rule to $\frac{14}{9}$ .

$\frac{\sqrt{15}}{3} + \frac{14^{2}}{9^{2}}$

Step 2.1.6

Raise $14$ to the power of $2$ .

$\frac{\sqrt{15}}{3} + \frac{196}{9^{2}}$

Step 2.1.7

Raise $9$ to the power of $2$ .

$\frac{\sqrt{15}}{3} + \frac{196}{81}$

Step 2.2

The expression is constant, which means it can be rewritten with a factor of $x^{0}$ . The degree is the largest exponent on the variable.

$0$

Step 3

A horizontal line does not rise or fall.

Straight line parallel to x-axis

Step 4