Perform the indicated operation. Assume that all variables represent non-negative real numbers -4√(8m)+7√(50m)

Question

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


`-4√(8m)+7√(50m)`

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√(8m) + 7√(50m) = -4√(2\cdot 4m) + 7√(2\cdot 25m)`

Now use the property
`√(ab) = √(a)√(b)\ \forall\ a,b\geq 0`

`-4√(4)√(2m) + 7√(25)√(2m) = -8√(2m)+35√(2m)`

Now we can factor
`√(2m)`:

`-8√(2m)+35√(2m) =√(2m)(-8+35) = 27√(2m)`