What is 3√-72
The expression 3√-72 represents the cube root of -72. Taking the cube root means finding the number that, when multiplied by itself twice, equals -72. However, there is no real number that satisfies this condition since (-4)^3 = -64 and (-3)^3 = -27. Thus, the cube root of -72 is not a real number.
To find the cube root of -72, follow these steps:
Step 1: Write down the number -72.
Step 2: Express -72 as a product of prime factors.
-72 = -1 x 2 x 2 x 2 x 3 x 3
Step 3: Group the prime factors into triplets, considering that we're calculating the cube root.
(2 x 2 x 2) x (3 x 3) x (-1)
Step 4: Simplify the expression.
2 x 3 x (-1) = -6
Therefore, the cube root of -72 is -6.
To find the value of the expression 3√(-72), we need to evaluate the cube root of -72.
First, let's break down the steps involved in finding the cube root of a number:
Step 1: Identify the prime factors of the number: The prime factors of -72 are -1, 2, 2, 2, and 3.
Step 2: Group the factors into triplets: Since we're calculating the cube root, we need to group the factors into triplets (three factors multiplied together).
In this case, we have one triplet: 2 × 2 × 2 = 8.
Step 3: Determine the product of the triplets: In our case, the product of the triplets is 8.
Step 4: Identify the sign: Since the number is negative, the cube root of -72 will be negative.
Putting it all together, we have:
3√(-72) = -2 × 3√8
Now, let's evaluate 3√8:
Finding the cube root of 8, we need to find a number that, when multiplied by itself three times, equals 8. The answer is 2, because 2 × 2 × 2 = 8.
Therefore, 3√8 = 2.
Finally, substitute this result back into the original expression:
3√(-72) = -2 × 3√8 = -2 × 2 = -4
Hence, the value of 3√(-72) is -4.