Simplify the Radical Expression 6/( square root of 3- square root of 2)

$\frac{6}{\sqrt{3} - \sqrt{2}}$

Step 1

Multiply $\frac{6}{\sqrt{3} - \sqrt{2}}$ by $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ .

$\frac{6}{\sqrt{3} - \sqrt{2}} \cdot \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$

Step 2

Multiply $\frac{6}{\sqrt{3} - \sqrt{2}}$ by $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ .

$\frac{6 (\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{6 (\sqrt{3} + \sqrt{2})}{{\sqrt{3}}^{2} + \sqrt{6} - \sqrt{6} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{6 (\sqrt{3} + \sqrt{2})}{1}$

Step 5

Divide $6 (\sqrt{3} + \sqrt{2})$ by $1$ .

$6 (\sqrt{3} + \sqrt{2})$

Step 6

Apply the distributive property.

$6 \sqrt{3} + 6 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{3} + 6 \sqrt{2}$

Decimal Form:

$18.87758621 \dots$