# How do I add radicals with different bases sqrt150 +sqrt40?

Apr 23, 2018

$\sqrt{150} + \sqrt{40} = \sqrt{2} \left(5 \sqrt{3} + 2 \sqrt{5}\right) = \sqrt{10 \left(19 + 4 \sqrt{15}\right)}$

#### Explanation:

Hmm. Not sure if this is what you want, but you could write this as a single, NESTED radical.

$\sqrt{150} + \sqrt{40} = \sqrt{{5}^{2} \left(3\right) \left(2\right)} + \sqrt{{2}^{2} \left(5\right) \left(2\right)}$

$= 5 \sqrt{3} \sqrt{2} + 2 \sqrt{5} \sqrt{2}$

$= \sqrt{2} \left(5 \sqrt{3} + 2 \sqrt{5}\right)$

$= \sqrt{2} \sqrt{{\left(5 \sqrt{3} + 2 \sqrt{5}\right)}^{2}}$

$= \sqrt{2} \sqrt{95 + 20 \sqrt{15}}$

$= \sqrt{2} \sqrt{5 \left(19 + 4 \sqrt{15}\right)}$

$= \sqrt{10 \left(19 + 4 \sqrt{15}\right)}$