SOLUTION: Simplify the following; express in terms of i sqrt -54 I got sqrt-54= 7.34846923i am I doing something wrong?

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify the following; express in terms of i sqrt -54 I got sqrt-54= 7.34846923i am I doing something wrong?       Log On


   

Question 625623: Simplify the following; express in terms of i
sqrt -54
I got sqrt-54= 7.34846923i
am I doing something wrong?
Found 2 solutions by reynard2007, josmiceli:
Answer by reynard2007(52) About Me  (Show Source):
You can put this solution on YOUR website!

That answer is actually right. But you can also simplify it by prime factoring -54. Doing that, we get sqrt%283%5E3%2A2%2A-1%29. We take the perfect square and the -1 out, we get sqrt%283%5E2%29%2Asqrt%283%2A2%29%2Asqrt%28-1%29. Simplify further and we end up with 9sqrt%286%29i.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+i+=+sqrt%28-1%29+
+sqrt%28-54%29+=+sqrt%28-1%29%2Asqrt%2854%29+
+sqrt%28-54%29+=+sqrt%28-1%29%2Asqrt%289%29%2Asqrt%286%29+
+sqrt%28-54%29+=+3%2Asqrt%286%29%2Ai+
and also
+sqrt%28-54%29+=+-3%2Asqrt%286%29%2Ai+
----------------------
To check, square both sides:
+%28sqrt%28-54%29%29%5E2+=+%283%2Asqrt%286%29%2Ai%29%5E2+
+-54+=+3%5E2%2A%28sqrt%286%29%29%5E2%2Ai%5E2+
+-54+=+9%2A6%2A%28-1%29+
+-54+=+-54+
OK
+%28sqrt%28-54%29%29%5E2+=+%28-3%2Asqrt%286%29%2Ai%29%5E2+
+-54+=+%28-3%29%5E2%2A%28sqrt%286%29%29%5E2%2Ai%5E2+
+-54+=+9%2A6%2A%28-1%29+
+-54+=+-54+
OK