# How do you simplify sqrt(250a^2) + sqrt(10a^2)?

May 7, 2015

Let's look at the two terms individually first:

$\textcolor{red}{\sqrt{250 {a}^{2}}} = \sqrt{25 \cdot 10 \cdot {a}^{2}}$

$= \sqrt{25} \cdot \sqrt{10} \cdot \sqrt{{a}^{2}}$ Because color(blue)(sqrt(ab) = sqrt a * sqrt b

 = 5*sqrt10*a = color(red)(5asqrt10

color(green)(sqrt(10a^2)) = sqrt10 * sqrt(a^2) = color(green)(asqrt10

Hence
$\textcolor{p u r p \le}{\sqrt{250 {a}^{2}} + \sqrt{10 {a}^{2}}} = 5 a \sqrt{10} + a \sqrt{10}$

$\sqrt{10}$ is common to both the terms

$= \sqrt{10} \left(5 a + a\right)$

$= \sqrt{10} \left(6 a\right)$

 = color(purple)(6asqrt10