Simplify, help please
sqrt-3 + sqrt27
To simplify the expression `sqrt(-3) + sqrt(27)`, we start by simplifying each square root separately.
First, let's simplify `sqrt(-3)`. The square root of a negative number is not a real number. However, we can rewrite it using the imaginary unit `i`, where `i = sqrt(-1)`. So, `sqrt(-3)` can be rewritten as `sqrt(3)i`.
Now let's simplify `sqrt(27)`. Since 27 is a perfect square, we can rewrite it as the square of a smaller number. `27` can be factored as `9 * 3`. We know that the square root of 9 is 3, so `sqrt(27)` can be simplified as `3 * sqrt(3)`.
Now we can substitute the simplified square roots back into the original expression:
`sqrt(-3) + sqrt(27) = sqrt(3)i + 3 * sqrt(3)`
To further simplify, notice that both terms have `sqrt(3)` as a common factor. We can factor it out:
`sqrt(3)i + 3 * sqrt(3) = sqrt(3)(i + 3)`
Therefore, the simplified expression is `sqrt(3)(i + 3)`.