simplify the following radical expression:
3 sqrt () -216x^2/x^2
a) sqrt() -6x
b)-6
c)-6 sqrt()x
d) 6 sqrt()-x
If I have read your data correctly (I'm not sure what "()" means), and there are no typos:
3 * √(-216x^2/x^2)
x^2's cancel each other out.
3 * √(-216)
This does not match any of your choices.
To simplify the given radical expression, we need to simplify the numerator and the denominator separately.
Let's start with the numerator, which is -216x^2. We can break it down by finding the largest perfect square factor of 216.
First, let's factor out the perfect squares:
216 = 6 * 6 * 6 = 6^2 * 6
Now, let's look at the variable x^2. Since x^2 is already a perfect square, we don't need to do anything with it.
Therefore, the numerator can be simplified as:
-216x^2 = -6^2 * 6 * x^2 = -6^2 * 6x^2
Moving on to the denominator, which is x^2. It is already in its simplest form.
Now, let's combine the simplified numerator and denominator:
-6^2 * 6x^2 / x^2 = -6^2 * 6 * x^2 / x^2 = -6^2 * 6 * x^2/x^2
Simplifying further, we have:
-36 * 6 * x^2/x^2 = -36 * 6 = -216
Therefore, the simplified radical expression is -216.
The correct answer is:
b) -6