# How do you simplify 5 times square root of 3 plus 4 times square root of 3?

Mar 14, 2018

$9 \sqrt{3} = {3}^{2.5}$

#### Explanation:

We have: $5 \sqrt{3} + 4 \sqrt{3}$.

We know that we can factor this, as $a b + a c = a \left(b + c\right)$.

So, we got

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

And so, we get

$= 9 \sqrt{3}$

If you want to simplify this further, we can do as follows.

$9 = {3}^{2}$

So, we have

$= {3}^{2} \sqrt{3}$

We also know that $\sqrt{x} = {x}^{\frac{1}{2}}$, so we have

$= {3}^{2} \cdot {3}^{\frac{1}{2}}$

We also can use the property that ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$, and we got

$= {3}^{2 + \frac{1}{2}}$

$= {3}^{2 \frac{1}{2}}$

$= {3}^{2.5}$

Mar 14, 2018

$9 \cdot \sqrt{3}$

#### Explanation:

You have $5 \cdot \sqrt{3} + 4 \cdot \sqrt{3}$.
This can be simplified to $9 \cdot \sqrt{3}$.

One simple way is to factor out the $\sqrt{3}$:
$5 \cdot \sqrt{3} + 4 \cdot \sqrt{3}$
$= \sqrt{3} \left(5 + 4\right)$
$= \sqrt{3} \left(9\right)$
$= 9 \cdot \sqrt{3}$

Mar 14, 2018

The simplified expression is $9 \sqrt{3}$.

#### Explanation:

First, translate the sentence from English to math:

$\stackrel{5}{\overbrace{\text{5") " " stackrel(xx) overbrace("times") " " stackrel(sqrt3) overbrace("square root of 3") " " stackrel(+) overbrace("plus") " " stackrel(4) overbrace("4") " " stackrel(xx) overbrace("times") " " stackrel(sqrt3) overbrace("square root of 3}}}$

Now, copy down the expression and simplify it. Since the $\sqrt{3}$'s are like terms, you can add together their coefficients.

$\textcolor{w h i t e}{=} 5 \times \sqrt{3} + 4 \times \sqrt{3}$

$= \textcolor{red}{5} \textcolor{b l u e}{\sqrt{3}} + \textcolor{red}{4} \textcolor{b l u e}{\sqrt{3}}$

$= \left(\textcolor{red}{5} + \textcolor{red}{4}\right) \textcolor{b l u e}{\sqrt{3}}$

$= \textcolor{red}{9} \textcolor{b l u e}{\sqrt{3}} \approx 15.588457 \ldots$

That's as simplified as it gets. Hope this is the answer you were looking for!