How do you simplify #5i sqrt(-54)# ?
3 Answers
Explanation:
Explanation:
We can take out the root of 9:
So we have:
So this gives:
Explanation:
Why another answer?
Because you should know that it is easy to make errors when it comes to square roots of negative (and complex) numbers.
The problem is that every non-zero number has two square roots, and the choice between them is a little arbitrary.
To see that there is a potential problem, consider the common "rule":
#sqrt(ab) = sqrt(a)sqrt(b)#
then note that:
#1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1) * sqrt(-1) = -1#
Ouch! The "rule" breaks if
Let's tread a little more carefully...
We use the symbol
If
If
#sqrt(n) = i sqrt(-n)#
where
With these conventions, we can safely state:
#sqrt(ab) = sqrt(a)sqrt(b)" if "a >= 0" or "b >= 0#
Then we find:
#5isqrt(-54) = 5i^2sqrt(54) = -5sqrt(3^2*6) = -5sqrt(3^2)sqrt(6) = -15sqrt(6)#