Simplify the number using the imaginary unit i.
square root -28
(1 point)
Responses
2 square root -7
Image with alt text: 2 square root -7
-2 square root -7
Image with alt text: -2 square root -7
i square root 28
Image with alt text: i square root 28
2i square root 7
Image: 2i square root 7
To simplify √(-28) using the imaginary unit (i), we can break down the square root into its factors:
√(-28) = √(4 * -7)
Since √4 = 2, we can simplify further:
√(-28) = 2√(-7)
Therefore, the simplified form of √(-28) using the imaginary unit i is 2√(-7).
To simplify the square root of -28 using the imaginary unit i, you can break it down into factors:
1. Start by factoring out the largest perfect square from 28, which is 4.
-28 = 4 * -7
2. Express the square root of -1 as i.
So, we have:
square root -28 = square root (4 * -7)
3. Split the square root into two separate square roots, using the property √(ab) = √a * √b:
square root -28 = square root 4 * square root -7
4. Simplify the square root of 4 to get 2:
square root -28 = 2 * square root -7
5. Finally, since the square root of -1 is represented by i, we can write:
square root -28 = 2i * square root 7
Therefore, the simplified form of the square root of -28 using the imaginary unit i is 2i * square root 7.