Question

HELP PLS 40 POINTS. IT HAS TWO ANSWERS TO IT MY TEACHER SAID. radical 75 + radical 18 - Radical 27 =

Answer 1

2 answers? maybe 2 different forms?

remember that
`a^(m)/(n)=\sqrt[n]{a^m}`

also, that
`√(ab)=(√(a))(√(b))`

and
`√(a^2)=a`

so factor each

75=3*5*5

18=2*3*3

27=3*3*3

`√(75)+√(18)-√(27)=`

`√((3)(5)(5))+√((2)(3)(3))-√((3)(3)(3))=`

`(√(3))(√(5))(√(5))+(√(2))(√(3))(√(3))-(√(3))(√(3))(√(3))=`

`(√(3))(5)+(√(2))(3)-(3)(√(3))=`

`5√(3)-3√(3)+3√(2)=`

`2√(3)+3√(2)`

not sure what the other solution is

you could go to back and factor out the √3 back there to get

`(√(3))(2+√(6))` but that's all I can see

Answer 2

sqrt(75) + sqrt(18) - sqrt(27)

sqrt(25*3) + sqrt(9*2) - sqrt(9*3)

sqrt(25) sqrt(3) + sqrt(9)sqrt(2) - sqrt(9)sqrt(3)

5sqrt(3) +3sqrt(2) -3sqrt(3)

5sqrt(3) - 3sqrt(3) + 3 sqrt(2)

2 sqrt(3) + 3 sqrt(2)