Finite Math Examples

$7.2 + 1.65 (\frac{2.2}{\sqrt{50}})$

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.1.1.1

Factor $25$ out of $50$ .

$7.2 + 1.65 \frac{2.2}{\sqrt{25 (2)}}$

Step 1.1.1.2

Rewrite $25$ as $5^{2}$ .

$7.2 + 1.65 \frac{2.2}{\sqrt{5^{2} \cdot 2}}$

Step 1.1.2

Pull terms out from under the radical.

$7.2 + 1.65 \frac{2.2}{5 \sqrt{2}}$

Step 1.2

Multiply $\frac{2.2}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$7.2 + 1.65 (\frac{2.2}{5 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}})$

Step 1.3

Combine and simplify the denominator.

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Step 1.3.1

Multiply $\frac{2.2}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 \sqrt{2} \sqrt{2}}$

Step 1.3.2

Move $\sqrt{2}$ .

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 (\sqrt{2} \sqrt{2})}$

Step 1.3.3

Raise $\sqrt{2}$ to the power of $1$ .

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 ({\sqrt{2}}^{1} \sqrt{2})}$

Step 1.3.4

Raise $\sqrt{2}$ to the power of $1$ .

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}$

Step 1.3.5

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

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 {\sqrt{2}}^{1 + 1}}$

Step 1.3.6

Add $1$ and $1$ .

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 {\sqrt{2}}^{2}}$

Step 1.3.7

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

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Step 1.3.7.1

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

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 {(2^{\frac{1}{2}})}^{2}}$

Step 1.3.7.2

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

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 \cdot 2^{\frac{1}{2} \cdot 2}}$

Step 1.3.7.3

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

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 \cdot 2^{\frac{2}{2}}}$

Step 1.3.7.4

Cancel the common factor of $2$ .

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Step 1.3.7.4.1

Cancel the common factor.

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 \cdot 2^{\frac{2}{2}}}$

Step 1.3.7.4.2

Rewrite the expression.

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 \cdot 2^{1}}$

Step 1.3.7.5

Evaluate the exponent.

$7.2 + 1.65 \frac{2.2 \sqrt{2}}{5 \cdot 2}$

Step 1.4

Multiply $2.2$ by $\sqrt{2}$ .

$7.2 + 1.65 \frac{3.11126983}{5 \cdot 2}$

Step 1.5

Multiply $5$ by $2$ .

$7.2 + 1.65 (\frac{3.11126983}{10})$

Step 1.6

Divide $3.11126983$ by $10$ .

$7.2 + 1.65 \cdot 0.31112698$

Step 1.7

Multiply $1.65$ by $0.31112698$ .

$7.2 + 0.51335952$

Step 2

Add $7.2$ and $0.51335952$ .

$7.71335952$