Question

Perform the indicated operation. Assume that all variables represent non-negative real numbers

Answer 1

Without a vale to substitute for the variable, we can only simplify the expression: since $8=4\cdot 2$ and $50 = 25\cdot 2$, the expression becomes

$-4\sqrt{8m} + 7\sqrt{50m} = -4\sqrt{2\cdot 4m} + 7\sqrt{2\cdot 25m}$

Now use the property $\sqrt{ab} = \sqrt{a}\sqrt{b}\ \forall\ a,b\geq 0$

$-4\sqrt{4}\sqrt{2m} + 7\sqrt{25}\sqrt{2m} = -8\sqrt{2m}+35\sqrt{2m}$

Now we can factor $\sqrt{2m}$:

$-8\sqrt{2m}+35\sqrt{2m} =\sqrt{2m}(-8+35) = 27\sqrt{2m}$