Simplify 6/( square root of 5+ square root of 3)

$\frac{6}{\sqrt{5} + \sqrt{3}}$

Multiply $\frac{6}{\sqrt{5} + \sqrt{3}}$ by $\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ .

$\frac{6}{\sqrt{5} + \sqrt{3}} \cdot \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}}$

Multiply $\frac{6}{\sqrt{5} + \sqrt{3}}$ by $\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ .

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

Expand the denominator using the FOIL method.

$\frac{6 (\sqrt{5} - \sqrt{3})}{{\sqrt{5}}^{2} - \sqrt{15} + \sqrt{15} - {\sqrt{3}}^{2}}$

Simplify.

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

Cancel the common factor of $6$ and $2$ .

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 (\sqrt{5} - \sqrt{3})}{1}$

Divide $3 (\sqrt{5} - \sqrt{3})$ by $1$ .

$3 (\sqrt{5} - \sqrt{3})$

Apply the distributive property.

$3 \sqrt{5} + 3 (- \sqrt{3})$

Multiply $- 1$ by $3$ .

$3 \sqrt{5} - 3 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5} - 3 \sqrt{3}$

Decimal Form:

$1.51205150 \dots$