Standard form for square root

Question

—4 plusminus +/- the square root of -108/6

Answer 1

-4 +or- sqrt(-108/6) = <-- GIVEN

-4 +or- sqrt( -648/36) = <-- rationalizes the denominator by multiplying by 6/6

-4 +or- sqrt(-1 * 648) / sqrt(36) <-- factors out -1 , so it gets ready for the imaginary i

-4 +or- sqrt(-1 * 6 * 108) / 6 <-- factors 648

-4 +or- sqrt(-1 * 6 * 12 * 9) / 6 <-- factors 108

-4 +or- sqrt(-1)*sqrt(6)*sqrt(12)sqrt(9)/ 6 <--- breaks them down into separate square roots

-4 +or- 3i* sqrt(6)*sqrt(12) / 6 <--- square root of 9 is 3; square root of -1 is i

-4 +or- 3i*sqrt(6)*sqrt(6) sqrt(2) / 6 <--- breaks down sqrt(12) = sqrt(2)sqrt(6)

-4 +or- 3i*6 * sqrt(2) / 6 <---6 cancels

-4 +or- 3i*sqrt(2) <-- DONE