express in terms of i and simplify: srqt-54 is it -3isqrt6?
Close. It can be either + or -
3i sqrt6
if you had to chose would it be the + or - or just select both?
Both
To express √(-54) in terms of i and simplify it, we first need to find the square root of -54.
Step 1: Write -54 as a product of its prime factors
-54 = -1 x 2 x 3² x i²
Step 2: Take the square root of each factor
√(-54) = √(-1) x √(2) x √(3²) x √(i²)
= i√(2) x 3 x i
= 3i²√(2)
= 3(-1)√(2) (since i² = -1)
= -3√(2)
Therefore, √(-54) is equal to -3√(2), not -3i√(6) as you previously stated.