Simplify the following number by using the imaginary number i

Question

sqrt -54

Answer 1

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