Calculus Examples

$\frac{10.2}{\sqrt{36 + {(10.2)}^{2}}} \cdot (440)$

Step 1

Simplify the denominator.

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Step 1.1

Raise $10.2$ to the power of $2$ .

$\frac{10.2}{\sqrt{36 + 104.04}} \cdot 440$

Step 1.2

Add $36$ and $104.04$ .

$\frac{10.2}{\sqrt{140.04}} \cdot 440$

Step 2

Multiply $\frac{10.2}{\sqrt{140.04}}$ by $\frac{\sqrt{140.04}}{\sqrt{140.04}}$ .

$\frac{10.2}{\sqrt{140.04}} \cdot \frac{\sqrt{140.04}}{\sqrt{140.04}} \cdot 440$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{10.2}{\sqrt{140.04}}$ by $\frac{\sqrt{140.04}}{\sqrt{140.04}}$ .

$\frac{10.2 \sqrt{140.04}}{\sqrt{140.04} \sqrt{140.04}} \cdot 440$

Step 3.2

Raise $\sqrt{140.04}$ to the power of $1$ .

$\frac{10.2 \sqrt{140.04}}{{\sqrt{140.04}}^{1} \sqrt{140.04}} \cdot 440$

Step 3.3

Raise $\sqrt{140.04}$ to the power of $1$ .

$\frac{10.2 \sqrt{140.04}}{{\sqrt{140.04}}^{1} {\sqrt{140.04}}^{1}} \cdot 440$

Step 3.4

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

$\frac{10.2 \sqrt{140.04}}{{\sqrt{140.04}}^{1 + 1}} \cdot 440$

Step 3.5

Add $1$ and $1$ .

$\frac{10.2 \sqrt{140.04}}{{\sqrt{140.04}}^{2}} \cdot 440$

Step 3.6

Rewrite ${\sqrt{140.04}}^{2}$ as $140.04$ .

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Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{140.04}$ as ${140.04}^{\frac{1}{2}}$ .

$\frac{10.2 \sqrt{140.04}}{{({140.04}^{\frac{1}{2}})}^{2}} \cdot 440$

Step 3.6.2

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

$\frac{10.2 \sqrt{140.04}}{{140.04}^{\frac{1}{2} \cdot 2}} \cdot 440$

Step 3.6.3

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

$\frac{10.2 \sqrt{140.04}}{{140.04}^{\frac{2}{2}}} \cdot 440$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{10.2 \sqrt{140.04}}{{140.04}^{\frac{2}{2}}} \cdot 440$

Step 3.6.4.2

Rewrite the expression.

$\frac{10.2 \sqrt{140.04}}{{140.04}^{1}} \cdot 440$

Step 3.6.5

Evaluate the exponent.

$\frac{10.2 \sqrt{140.04}}{140.04} \cdot 440$

Step 4

Multiply $10.2$ by $\sqrt{140.04}$ .

$\frac{120.70526749}{140.04} \cdot 440$

Step 5

Simplify the expression.

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Step 5.1

Divide $120.70526749$ by $140.04$ .

$0.86193421 \cdot 440$

Step 5.2

Multiply $0.86193421$ by $440$ .

$379.25105466$