Simplify 6/( square root of 5- square root of 2)

$\frac{6}{\sqrt{5} - \sqrt{2}}$

Multiply $\frac{6}{\sqrt{5} - \sqrt{2}}$ by $\frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$ .

$\frac{6}{\sqrt{5} - \sqrt{2}} \cdot \frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$

Multiply $\frac{6}{\sqrt{5} - \sqrt{2}}$ by $\frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$ .

$\frac{6 (\sqrt{5} + \sqrt{2})}{(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})}$

Expand the denominator using the FOIL method.

$\frac{6 (\sqrt{5} + \sqrt{2})}{{\sqrt{5}}^{2} + \sqrt{10} - \sqrt{10} - {\sqrt{2}}^{2}}$

Simplify.

$\frac{6 (\sqrt{5} + \sqrt{2})}{3}$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 (\sqrt{5} + \sqrt{2})$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 (\sqrt{5} + \sqrt{2}))}{3 (1)}$

Cancel the common factor.

$\frac{3 (2 (\sqrt{5} + \sqrt{2}))}{3 \cdot 1}$

Rewrite the expression.

$\frac{2 (\sqrt{5} + \sqrt{2})}{1}$

Divide $2 (\sqrt{5} + \sqrt{2})$ by $1$ .

$2 (\sqrt{5} + \sqrt{2})$

Apply the distributive property.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$7.30056307 \dots$