simplify the following radical expression: 3 sqrt (-27)
a) -3
b) 3
c) 0
d) no solution exists
do i write the sqrt like this or do i write like this sqrt () 3 -27 please show me the correct way to write it thanks
The way you wrote it, I interpret it as:
3√(-27).
Since it is impossible to square a real number and get a negative result, there is no solution in the real domain.
alright thanks mathmate
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To simplify the radical expression 3√(-27), let's break it down step by step:
1. Start by simplifying the square root of the number inside the radical symbol. In this case, 27 is a perfect cube, so we can write it as 3^3.
√27 = √(3^3)
2. Now, let's consider the negative sign. A square root of a negative number is not possible in the real number system because the square of any real number is always positive. However, since we are dealing with the cube root (√3), which requires three instances of the same number multiplied together, a negative value is allowed.
3. Simplify the cube root of 3^3:
√(3^3) = 3
4. Now, add the negative sign to the final result since we had a negative radicand:
3√(-27) = -3
So, the simplified radical expression 3√(-27) is equal to -3.
To write the radical expression correctly, it should be written as: 3√(-27).