Calculus Examples

$\frac{{3.2}^{2} - 10}{3.2 - \sqrt{10}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $3.2$ to the power of $2$ .

$\frac{10.24 - 10}{3.2 - \sqrt{10}}$

Step 1.2

Subtract $10$ from $10.24$ .

$\frac{0.24}{3.2 - \sqrt{10}}$

Step 2

Multiply $\frac{0.24}{3.2 - \sqrt{10}}$ by $\frac{3.2 + \sqrt{10}}{3.2 + \sqrt{10}}$ .

$\frac{0.24}{3.2 - \sqrt{10}} \cdot \frac{3.2 + \sqrt{10}}{3.2 + \sqrt{10}}$

Step 3

Multiply $\frac{0.24}{3.2 - \sqrt{10}}$ by $\frac{3.2 + \sqrt{10}}{3.2 + \sqrt{10}}$ .

$\frac{0.24 (3.2 + \sqrt{10})}{(3.2 - \sqrt{10}) (3.2 + \sqrt{10})}$

Step 4

Expand the denominator using the FOIL method.

$\frac{0.24 (3.2 + \sqrt{10})}{10.24 + 10.11928851 - 10.11928851 - {\sqrt{10}}^{2}}$

Step 5

Simplify.

$\frac{0.24 (3.2 + \sqrt{10})}{0.24}$

Step 6

Cancel the common factor of $0.24$ and $0.24$ .

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Step 6.1

Cancel the common factor.

$\frac{0.24 (3.2 + \sqrt{10})}{0.24}$

Step 6.2

Divide $3.2 + \sqrt{10}$ by $1$ .

$3.2 + \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$3.2 + \sqrt{10}$

Decimal Form:

$6.36227766 \dots$