∛-72 simplified
∛-72 simplifies to -4.
To simplify the cube root of -72 (∛-72), we need to find the prime factors of -72 and then group them in sets of three.
First, let's determine the prime factorization of 72:
72 = 2 x 2 x 2 x 3 x 3
Now, since we are looking for the cube root, we need to group the prime factors in sets of three:
(2 x 2 x 2) x (3 x 3)
Simplifying, we have:
2 x 3 = 6
Therefore, the simplified cube root of -72 (∛-72) is 6.
To simplify ∛-72, we need to find the cube root of -72. The cube root of a number is the value that, when multiplied by itself three times, equals the given number.
To calculate the cube root of -72, follow these steps:
Step 1: Write -72 as a product of prime factors:
-72 = -1 × 2 × 2 × 2 × 3 × 3
Step 2: Group the prime factors into sets of three, taking the highest possible grouping:
-72 = -1 × (2 × 2 × 2) × (3 × 3)
Step 3: Take out any sets of three from the prime factors and bring them out of the cube root:
∛-72 = ∛(-1 × (2 × 2 × 2) × (3 × 3))
∛-72 = -1 × 2 × 3 × ∛(2 × 2 × 2 × 3 × 3)
Step 4: Simplify the cube root of the remaining factors:
∛(2 × 2 × 2 × 3 × 3) = 2 × 3 = 6
Step 5: Multiply the factors outside the cube root:
-1 × 2 × 3 × 6 = -36
Therefore, the simplified cube root of -72 is -36.
incorrect
I apologize for the incorrect response. Let's simplify ∛-72 correctly:
Since -72 is a negative number, we can find the cube root of its absolute value, simplify it, and then negate the result.
The absolute value of -72 is 72. Now, let's find the prime factorization of 72:
72 = 2 x 2 x 2 x 3 x 3
We can group the prime factors in sets of three:
(2 x 2 x 2) x (3 x 3)
Simplifying, we have:
2 x 3 = 6
Therefore, the simplified cube root of -72 (∛-72) is -6.
incorrect
I apologize for the confusion. Let's simplify ∛-72 correctly:
Since -72 is a negative number, we can find the cube root of its absolute value and then negate the result.
The absolute value of -72 is 72. Now, let's find the prime factorization of 72:
72 = 2 x 2 x 2 x 3 x 3
We can group the prime factors in sets of three:
(2 x 2 x 2) x (3 x 3)
Simplifying, we have:
2 x 3 = 6
Therefore, the simplified cube root of -72 (∛-72) is -6.
wrong wrong WRONG~!
Apologies for the previous incorrect responses. Let's simplify ∛-72 correctly:
To simplify the cube root of -72 (∛-72), we can factor out the largest perfect cube from -72.
The largest perfect cube that can be factored out of -72 is -8, which is the cube of -2: -8 = (-2)^3.
We can rewrite -72 as:
-72 = -8 x 9 = (-2)^3 x (3^2)
Taking the cube root of -72:
∛-72 = ∛(-2)^3 x (3^2)
Using the property of cube roots that (∛a)^3 = a, we can simplify:
∛-72 = -2 x ∛9
Therefore, the simplified cube root of -72 (∛-72) is -2∛9.