# How do you simplify 8sqrt3+5sqrt3?

Dec 22, 2016

$13 \sqrt{3}$

#### Explanation:

you can simplify $8 \sqrt{3}$ and $5 \sqrt{3}$ by collecting like terms.

$8 \sqrt{3}$ and $5 \sqrt{3}$ are like terms- they are both multiples of $\sqrt{3}$.

$8 + 5 = 13$, so the result is $13 \cdot \sqrt{3}$ or $13 \sqrt{3}$.

Dec 22, 2016

$13 \sqrt{3}$

#### Explanation:

Radicals can be treated in a similar way to algebraic terms in that we can add/subtract $\textcolor{b l u e}{\text{like radicals}}$

$\text{Example } 8 x + 5 x$ are like terms since they both contain the same variable x
We can therefore collect them together by adding their coefficients.

That is 8x + 5x = (8 + 5)x = 13x

$\sqrt{3}$ in both terms are considered like radicals as they have different values to $\sqrt{2} , \sqrt{6} \text{ etc }$

$\Rightarrow 8 \sqrt{3} + 5 \sqrt{3} = \left(8 + 5\right) \sqrt{3} = 13 \sqrt{3}$