# How do you simplify (1-sqrt3) (3+ sqrt2)?

Feb 7, 2016

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

#### Explanation:

Use the FOIL method of multiplying Binomials:

$\left(1 - \sqrt{3}\right) \left(3 + \sqrt{2}\right)$

$\underline{F} i r s t s$

$\rightarrow = 1 \cdot 3 = 3$

$\underline{O} u t e r$

$\rightarrow = 1 \cdot \sqrt{2} = \sqrt{2}$

$\underline{I}$$n$$n$$e r$

$\rightarrow = - \sqrt{3} \cdot 3 = - 3 \sqrt{3}$

$\underline{L}$$a$$s t$

$\rightarrow = - \sqrt{3} \cdot \sqrt{2} = - \sqrt{6}$

Now put them all together:

$\left(1 - \sqrt{3}\right) \left(3 + \sqrt{2}\right) = 3 + \sqrt{2} - 3 \sqrt{3} - \sqrt{6}$