Question

write in terms of i: √-54

Answer 1

can you prime factor 54?

Answer 2

√9*6
√9√6
3√6

Answer 3

3*3*3*2

Answer 4

Yes, now you need to take the sqrt(-1) with the 3.
You'd have 3i * sqrt(6)

Answer 5

-3√6

Answer 6

More accurately it might look like:
\[\sqrt(-9 * 6) = \sqrt(-9) * \sqrt(6) = 3i \sqrt(6)\]

Answer 7

so the i replaces the negative sign?

Answer 8

Since there is no real solution to the square root of an even number we say that there's an imaginary component. So the real root is 3, with the imaginary 'i'

Answer 9

no real solution to the square root of a negative number*

Answer 10

ok so it would be 3i√6

Answer 11

Correct.

Answer 12

ok thank you