Algebra Examples

$\frac{\sqrt{13} + 3}{8}$

Step 1

Multiply to rationalize the numerator.

$\frac{(\sqrt{13} + 3) (\sqrt{13} - 3)}{8 (\sqrt{13} - 3)}$

Step 2

Simplify.

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Step 2.1

Expand the numerator using the FOIL method.

$\frac{{\sqrt{13}}^{2} + \sqrt{13} \cdot - 3 + \sqrt{13} \cdot 3 - 9}{8 (\sqrt{13} - 3)}$

Step 2.2

Simplify.

$\frac{4}{8 (\sqrt{13} - 3)}$

Step 3

Apply the distributive property.

$\frac{4}{8 \sqrt{13} + 8 \cdot - 3}$

Step 4

Multiply $8$ by $- 3$ .

$\frac{4}{8 \sqrt{13} - 24}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{8 \sqrt{13} - 24}$

Decimal Form:

$0.82569390 \dots$