Step-by-step explanation: The prime factorization of 4320 is
2•2•2•2•2•3•3•3•5
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 4320 = √ 2•2•2•2•2•3•3•3•5 =2•2•3•√ 30 =
± 12 • √ 30
√ 30 , rounded to 4 decimal digits, is 5.4772
So now we are looking at:
w = ( -40 ± 12 • 5.477 ) / -34
Two real solutions:
w =(-40+√4320)/-34=(20-6√ 30 )/17= -0.757
or:
w =(-40-√4320)/-34=(20+6√ 30 )/17= 3.110
MY HEAD HURTS!
