Simplify the following number by using the imaginary number i
sqrt -54
To simplify the square root of -54 using the imaginary number i, we can first rewrite -54 as -1 * 54:
√(-54) = √(-1 * 54)
Next, we can break down the square root of -1 and 54 separately:
√(-1 * 54) = √-1 * √54
Since the square root of -1 is defined as i, we can substitute it:
√(-1 * 54) = i * √54
Now, we can simplify the square root of 54. The largest perfect square that divides evenly into 54 is 9:
√54 = √(9 * 6) = √9 * √6 = 3 * √6
Therefore, the simplified form is:
√(-54) = i * (√54) = i * (3 * √6) = 3i * √6