How do you simplify (6+sqrt128)/2?

Jul 10, 2015

$= \textcolor{b l u e}{3 + \sqrt{32}}$

Explanation:

sqrt128 = color(green)(sqrt(4 * 32)
The expression can be written as:

$\left(\frac{6 + \textcolor{g r e e n}{\sqrt{4 \cdot 32}}}{2}\right)$

$= \left(\frac{6 + 2 \left(\sqrt{32}\right)}{2}\right)$

$2$ is common to both terms of the numerator:

$= \cancel{2} \left(\frac{3 + \left(\sqrt{32}\right)}{\cancel{2}}\right)$

$= \textcolor{b l u e}{3 + \sqrt{32}}$