Express in terms of i and simplify:
sqrt-54
is the answer -3isqrt6
To express sqrt(-54) in terms of i and simplify it, we can start by factoring -54.
-54 can be factored as -1 * 54 or -1 * 2 * 27.
Now, let's simplify sqrt(-54):
sqrt(-54) = sqrt(-1 * 2 * 27)
Since sqrt(-1) is not a real number, we can rewrite it as i, the imaginary unit:
sqrt(-54) = sqrt(-1) * sqrt(2) * sqrt(27)
Using the property of square roots, we can split the square root of a product into the product of square roots:
sqrt(-54) = i * sqrt(2) * sqrt(3^3)
Now, simplifying further:
sqrt(-54) = i * sqrt(2) * 3 * sqrt(3)
= 3i * sqrt(6)
So, the simplified form of sqrt(-54) is 3i * sqrt(6).
Note: In the original question, you mentioned that the answer is -3i * sqrt(6). However, the correct answer is 3i * sqrt(6) since the square root of -54 does not contain a real part, only the imaginary part with 3i.