Simplify 3/( square root of 17- square root of 2)

$\frac{3}{\sqrt{17} - \sqrt{2}}$

Step 1

Multiply $\frac{3}{\sqrt{17} - \sqrt{2}}$ by $\frac{\sqrt{17} + \sqrt{2}}{\sqrt{17} + \sqrt{2}}$ .

$\frac{3}{\sqrt{17} - \sqrt{2}} \cdot \frac{\sqrt{17} + \sqrt{2}}{\sqrt{17} + \sqrt{2}}$

Step 2

Multiply $\frac{3}{\sqrt{17} - \sqrt{2}}$ by $\frac{\sqrt{17} + \sqrt{2}}{\sqrt{17} + \sqrt{2}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (\sqrt{17} + \sqrt{2})}{{\sqrt{17}}^{2} + \sqrt{34} - \sqrt{34} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{3 (\sqrt{17} + \sqrt{2})}{15}$

Step 5

Cancel the common factors.

Factor $3$ out of $15$ .

$\frac{3 (\sqrt{17} + \sqrt{2})}{3 \cdot 5}$

Cancel the common factor.

$\frac{3 (\sqrt{17} + \sqrt{2})}{3 \cdot 5}$

Rewrite the expression.

$\frac{\sqrt{17} + \sqrt{2}}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{17} + \sqrt{2}}{5}$

Decimal Form:

$1.10746383 \dots$