What is ³√-72 simplified.
The cube root of -72 simplified is -2 multiplied by the cube root of 9.
To simplify the cube root of -72, follow these steps:
Step 1: Find the prime factorization of the number inside the cube root symbol.
The prime factorization of -72 is -1 x 2 x 2 x 2 x 3 x 3.
Step 2: Group the prime factors in sets of three.
Since there are no sets of three prime factors, we can't simplify the cube root any further.
So, the simplified form of the cube root of -72 is still ³√-72.
To simplify the cube root of -72, we need to find the largest perfect cube that can be extracted from -72.
First, let's factor -72 into prime factors. We can start by factoring it into -1 * 72, and further factorize 72 into 2 * 2 * 2 * 3 * 3.
So, -72 = -1 * 2 * 2 * 2 * 3 * 3.
Now, we can group the prime factors into sets of threes, as we are finding the cube root:
-72 = (-1) * (2 * 2 * 2) * (3 * 3)
Now, we can simplify each group by performing the cube root operation:
-72 simplified = (-1) * (2 * 2 * 2) * (3 * 3) = -1 * 2 * 3 * 3 = -18
Therefore, the simplified cube root of -72 is -18.