# How do you simplify (5+4sqrt3)(3+sqrt3)?

Apr 11, 2018

Foil and combine like terms

#### Explanation:

Start by foiling. You should get $15 + 5 \sqrt{3} + 12 \sqrt{3} + 12$. If you're not sure how I got 12 it's because when you multiply roots they cancel so $\sqrt{3}$ times $\sqrt{3}$ became 3, and that 3 got multiplied by the 4 to become 12. Once you have $15 + 5 \sqrt{3} + 12 \sqrt{3} + 12$, you have to combine like terms so you get $17 \sqrt{3} + 27$.

Apr 11, 2018

$= 17 \sqrt{3} + 27$

#### Explanation:

Using the FOIL method, you can multiply the two terms together using the numbers inside each set of parenthesis.

$\left(5 + 4 \sqrt{3}\right) \left(3 + \sqrt{3}\right)$

F means "first terms."

$5 \cdot 3 = 15$

I means "inner terms."

$4 \sqrt{3} \cdot 3 = 12 \sqrt{3}$

O means "outer terms."

$5 \cdot \sqrt{3} = 5 \sqrt{3}$

Finally, L means "last terms."

$4 \sqrt{3} \cdot \sqrt{3} = 4 \cdot 3 = 12$

$15 + 12 \sqrt{3} + 5 \sqrt{3} + 12$

$= 17 \sqrt{3} + 27$

That is the expanded form.