Question

How do you simplify `2* sqrt(-1/6) + sqrt(-4/3)`?

Answer 1

`isqrt(3)/3(sqrt(2)+4 )`

Explanation:

Simplify: `2*sqrt(-1/6)+sqrt(-4/3)`
`2*isqrt(1/6)+isqrt(4/3)`
`2/sqrt(2)*isqrt(1/3)+isqrt(4/3)`
`(2i)[1/(sqrt(2)sqrt(3))+sqrt(4)/sqrt(3)] = 2i(1+2sqrt(2))/(sqrt(6)`
Multiply top and bottom by `sqrt(6)`
`2i(1+2sqrt(2))/(sqrt(6))*sqrt(6)/sqrt(6)= 2i(sqrt(6)+2sqrt(3)sqrt(2)*sqrt(2))/(sqrt(6)*sqrt(6)`

`2i(sqrt(2)sqrt(3)+4sqrt(3))/(6)=isqrt(3)/3(sqrt(2)+4 )`