Finite Math Examples

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

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

Step 1

Write

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

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

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

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

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}}

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

\frac{\sqrt{5}}{\sqrt{3}}

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

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

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

Step 2.1.2

Multiply

\frac{\sqrt{5}}{\sqrt{3}}

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

\frac{\sqrt{3}}{\sqrt{3}}

$\frac{\sqrt{3}}{\sqrt{3}}$ .

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

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

Step 2.1.3

Combine and simplify the denominator.

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Step 2.1.3.1

Multiply

\frac{\sqrt{5}}{\sqrt{3}}

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

\frac{\sqrt{3}}{\sqrt{3}}

$\frac{\sqrt{3}}{\sqrt{3}}$ .

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

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

Step 2.1.3.2

Raise

\sqrt{3}

$\sqrt{3}$ to the power of

1

$1$ .

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

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

Step 2.1.3.3

Raise

\sqrt{3}

$\sqrt{3}$ to the power of

1

$1$ .

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

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

Step 2.1.3.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 2.1.3.5

Add

1

$1$ and

1

$1$ .

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

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

Step 2.1.3.6

Rewrite

{\sqrt{3}}^{2}

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

3

$3$ .

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Step 2.1.3.6.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{3}

$\sqrt{3}$ 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