Calculus Examples

$\frac{490 + \sqrt{240100 + 403200}}{84}$

Step 1

Simplify the numerator.

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Step 1.1

Add $240100$ and $403200$ .

$\frac{490 + \sqrt{643300}}{84}$

Step 1.2

Rewrite $643300$ as $10^{2} \cdot 6433$ .

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Step 1.2.1

Factor $100$ out of $643300$ .

$\frac{490 + \sqrt{100 (6433)}}{84}$

Step 1.2.2

Rewrite $100$ as $10^{2}$ .

$\frac{490 + \sqrt{10^{2} \cdot 6433}}{84}$

$\frac{490 + \sqrt{10^{2} \cdot 6433}}{84}$

Step 1.3

Pull terms out from under the radical.

$\frac{490 + 10 \sqrt{6433}}{84}$

$\frac{490 + 10 \sqrt{6433}}{84}$

Step 2

Cancel the common factor of $490 + 10 \sqrt{6433}$ and $84$ .

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Step 2.1

Factor $2$ out of $490$ .

$\frac{2 (245) + 10 \sqrt{6433}}{84}$

Step 2.2

Factor $2$ out of $10 \sqrt{6433}$ .

$\frac{2 (245) + 2 (5 \sqrt{6433})}{84}$

Step 2.3

Factor $2$ out of $2 (245) + 2 (5 \sqrt{6433})$ .

$\frac{2 (245 + 5 \sqrt{6433})}{84}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $84$ .

$\frac{2 (245 + 5 \sqrt{6433})}{2 \cdot 42}$

Step 2.4.2

Cancel the common factor.

$\frac{2 (245 + 5 \sqrt{6433})}{2 \cdot 42}$

Step 2.4.3

Rewrite the expression.

$\frac{245 + 5 \sqrt{6433}}{42}$

$\frac{245 + 5 \sqrt{6433}}{42}$

$\frac{245 + 5 \sqrt{6433}}{42}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{245 + 5 \sqrt{6433}}{42}$

Decimal Form:

$15.38166485 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$