simplify the following radical expression: 3 sqrt (-27)
a) 0
b) -3
c) 3
d) no solution exists
we cannot take the square root of a negative number, so d)
3sqrt(-27)=3sqrt(9*3*-1)=3*3i*sqrt3=
9i*sqrt3. imagenary solution: d
To simplify the radical expression 3 √(-27), we first need to simplify the inside of the square root.
We can rewrite -27 as -1 * 3^3 to find its prime factorization. Taking the square root, we get:
3 √(-1 * 3^3)
Next, we can simplify the cube root by breaking it down into separate root terms for the numbers inside. We have:
3 √(-1) * √(3^3)
The square root of -1 is equal to the imaginary unit, denoted as "i". Therefore, we can simplify further:
3i * √(3^3)
Now, calculating the cube root of 3^3, we get:
3i * 3 = 9i
So, the simplified form of 3 √(-27) is 9i.
Therefore, the correct answer would be (d) no solution exists, as none of the given options match the simplified form of the expression.