Finite Math Examples

$2 (- \frac{5}{11}) (\sqrt{\frac{96}{11}})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Multiply

$2 (- \frac{5}{11})$ .

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Step 1.1.1

Multiply

$- 1$ by

$2$ .

$- 2 (\frac{5}{11}) \sqrt{\frac{96}{11}}$

Step 1.1.2

Combine

$- 2$ and

$\frac{5}{11}$ .

$\frac{- 2 \cdot 5}{11} \sqrt{\frac{96}{11}}$

Step 1.1.3

Multiply

$- 2$ by

$5$ .

$\frac{- 10}{11} \sqrt{\frac{96}{11}}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{10}{11} \sqrt{\frac{96}{11}}$

Step 1.3

Rewrite

$\sqrt{\frac{96}{11}}$ as

$\frac{\sqrt{96}}{\sqrt{11}}$ .

$- \frac{10}{11} \cdot \frac{\sqrt{96}}{\sqrt{11}}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Rewrite

$96$ as

$4^{2} \cdot 6$ .

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Step 1.4.1.1

Factor

$16$ out of

$96$ .

$- \frac{10}{11} \cdot \frac{\sqrt{16 (6)}}{\sqrt{11}}$

Step 1.4.1.2

Rewrite

$16$ as

$4^{2}$ .

$- \frac{10}{11} \cdot \frac{\sqrt{4^{2} \cdot 6}}{\sqrt{11}}$

Step 1.4.2

Pull terms out from under the radical.

$- \frac{10}{11} \cdot \frac{4 \sqrt{6}}{\sqrt{11}}$

Step 1.5

Multiply

$\frac{4 \sqrt{6}}{\sqrt{11}}$ by

$\frac{\sqrt{11}}{\sqrt{11}}$ .

$- \frac{10}{11} (\frac{4 \sqrt{6}}{\sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}})$

Step 1.6

Combine and simplify the denominator.

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Step 1.6.1

Multiply

$\frac{4 \sqrt{6}}{\sqrt{11}}$ by

$\frac{\sqrt{11}}{\sqrt{11}}$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{\sqrt{11} \sqrt{11}}$

Step 1.6.2

Raise

$\sqrt{11}$ to the power of

$1$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{{\sqrt{11}}^{1} \sqrt{11}}$

Step 1.6.3

Raise

$\sqrt{11}$ to the power of

$1$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{{\sqrt{11}}^{1} {\sqrt{11}}^{1}}$

Step 1.6.4

Use the power rule

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

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{{\sqrt{11}}^{1 + 1}}$

Step 1.6.5

Add

$1$ and

$1$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{{\sqrt{11}}^{2}}$

Step 1.6.6

Rewrite

${\sqrt{11}}^{2}$ as

$11$ .

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Step 1.6.6.1

Use

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

$\sqrt{11}$ as

$11^{\frac{1}{2}}$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{{(11^{\frac{1}{2}})}^{2}}$

Step 1.6.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{11^{\frac{1}{2} \cdot 2}}$

Step 1.6.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{11^{\frac{2}{2}}}$

Step 1.6.6.4

Cancel the common factor of

$2$ .

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Step 1.6.6.4.1

Cancel the common factor.

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{11^{\frac{2}{2}}}$

Step 1.6.6.4.2

Rewrite the expression.

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{11^{1}}$

Step 1.6.6.5

Evaluate the exponent.

$- \frac{10}{11} \cdot \frac{4 \sqrt{6} \sqrt{11}}{11}$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Combine using the product rule for radicals.

$- \frac{10}{11} \cdot \frac{4 \sqrt{11 \cdot 6}}{11}$

Step 1.7.2

Multiply

$11$ by

$6$ .

$- \frac{10}{11} \cdot \frac{4 \sqrt{66}}{11}$

Step 1.8

Multiply

$- \frac{10}{11} \cdot \frac{4 \sqrt{66}}{11}$ .

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Step 1.8.1

Multiply

$\frac{4 \sqrt{66}}{11}$ by

$\frac{10}{11}$ .

$- \frac{4 \sqrt{66} \cdot 10}{11 \cdot 11}$

Step 1.8.2

Multiply

$10$ by

$4$ .

$- \frac{40 \sqrt{66}}{11 \cdot 11}$

Step 1.8.3

Multiply

$11$ by

$11$ .

$- \frac{40 \sqrt{66}}{121}$

Step 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.

$0$