Simplify the number using the imaginary unit i:
(square root) -28
options:
a. 2(square root) -7
b. -2(square root) -7
c. i(square root) 28
d. 2i(square root) 28
answer 1 - 6
The answer is c. i(square root) 28.
To simplify the square root of -28 using the imaginary unit i, first, factor out the largest perfect square from -28, which is 4:
√(-28) = √(-1 × 4 × 7)
Next, we can rewrite the square root of -1 as i:
√(-1 × 4 × 7) = √(-1) × √(4) × √(7) = i × 2 × √(7)
Finally, we can simplify it further:
i × 2 × √(7) = 2i√(7)
Therefore, the answer is option d) 2i√(7).
To simplify the number using the imaginary unit i, we need to express the number in terms of imaginary unit i.
The square root of a negative number can be written as the product of the square root of the positive value and the imaginary unit i.
Let's simplify the square root of -28:
√(-28) = √(28) * √(-1)
The square root of 28 can be simplified as √(28) = 2√(7).
So, the simplified form of the square root of -28 becomes:
√(-28) = 2√(7) * i
Now, let's check the given options:
a. 2√(-7)
b. -2√(-7)
c. i√(28)
d. 2i√(28)
Among the options, the correct answer is c. i√(28), because we have expressed the negative square root of -28 as a positive square root of 28, multiplied by the imaginary unit i.