# How do you simplify sqrt(3a) + 2sqrt(27a^3)?

Jun 22, 2016

sqrt(3a)+2sqrt(27a^3)=color(green)((1+6a)(sqrt(3a))

#### Explanation:

$2 \sqrt{27 {a}^{3}} = 2 \cdot \sqrt{{3}^{2} \cdot 2 \cdot {a}^{2} \cdot a}$
$\textcolor{w h i t e}{\text{XXX}} = 2 \cdot \sqrt{{\left(3 a\right)}^{2}} \cdot \sqrt{3 a}$
$\textcolor{w h i t e}{\text{XXX}} = 6 a \sqrt{3 a}$

So
$\sqrt{3 a} + 2 \sqrt{27 {a}^{3}}$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{3 a} + 6 a \sqrt{3 a}$
$\textcolor{w h i t e}{\text{XXX}} = \left(1 + 6 a\right) \sqrt{3 a}$

Jun 22, 2016

$\sqrt{3 a} \left(6 a + 1\right)$

#### Explanation:

Notice that $3 \times 9 = 27 \to 3 \times {3}^{3} = 27$
Also notice that ${a}^{3} = {a}^{2} \times a$

Write as:
$\sqrt{3 a} + 2 \sqrt{{3}^{2} {a}^{2} \times 3 a}$

Take the ${3}^{3} {a}^{a}$ outside the square root as $\sqrt{{3}^{2} {a}^{2}} = 3 a$

$\sqrt{3 a} + \left(3 a \times 2 \times \sqrt{3 a}\right)$

$\sqrt{3 a} + 6 a \sqrt{3 a}$

Factor out the $\sqrt{3 a}$

$\sqrt{3 a} \left(1 + 6 a\right)$

Or if you prefer

$\sqrt{3 a} \left(6 a + 1\right)$