Precalculus Examples

$\frac{\sqrt{3}}{\sqrt{17} + 3}$

Step 1

Multiply $\frac{\sqrt{3}}{\sqrt{17} + 3}$ by $\frac{\sqrt{17} - 3}{\sqrt{17} - 3}$ .

$\frac{\sqrt{3}}{\sqrt{17} + 3} \cdot \frac{\sqrt{17} - 3}{\sqrt{17} - 3}$

Step 2

Simplify terms.

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Step 2.1

Multiply $\frac{\sqrt{3}}{\sqrt{17} + 3}$ by $\frac{\sqrt{17} - 3}{\sqrt{17} - 3}$ .

$\frac{\sqrt{3} (\sqrt{17} - 3)}{(\sqrt{17} + 3) (\sqrt{17} - 3)}$

Step 2.2

Expand the denominator using the FOIL method.

$\frac{\sqrt{3} (\sqrt{17} - 3)}{{\sqrt{17}}^{2} + \sqrt{17} \cdot - 3 + 3 \sqrt{17} - 9}$

Step 2.3

Simplify.

$\frac{\sqrt{3} (\sqrt{17} - 3)}{8}$

Step 2.4

Apply the distributive property.

$\frac{\sqrt{3} \sqrt{17} + \sqrt{3} \cdot - 3}{8}$

Step 2.5

Combine using the product rule for radicals.

$\frac{\sqrt{3 \cdot 17} + \sqrt{3} \cdot - 3}{8}$

Step 2.6

Move $- 3$ to the left of $\sqrt{3}$ .

$\frac{\sqrt{3 \cdot 17} - 3 \cdot \sqrt{3}}{8}$

Step 3

Multiply $3$ by $17$ .

$\frac{\sqrt{51} - 3 \sqrt{3}}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{51} - 3 \sqrt{3}}{8}$

Decimal Form:

$0.24315950 \dots$