How do you simplify 3sqrt6-24+2sqrt150?

May 18, 2018

$13 \sqrt{6} - 24$

Explanation:

Please note that $150 = 25 \cdot 6 = {5}^{2} \cdot 6$
Therefore $2 \sqrt{150} = 2 \cdot 5 \sqrt{6} = 10 \sqrt{6}$
Therefore $3 \sqrt{6} - 24 + 2 \sqrt{150} = 13 \sqrt{6} - 24$

We can, of course, write $24 = 4 \cdot 6 = 4 {\left(\sqrt{6}\right)}^{2}$,
but $\left(13 - 4 \sqrt{6}\right) \sqrt{6}$ can hardly be said to be more simplified.