What is ∛-72 simplified?
The cube root of -72 simplified is -4.
To simplify the cube root of -72, follow these steps:
Step 1: Find the prime factorization of 72.
72 = 2 × 2 × 2 × 3 × 3
Step 2: Group the prime factors in triples.
72 = 2 × 2 × 2 × 3 × 3 = 2^3 × 3^2
Step 3: Write the cube root of -72.
∛(-72)
Step 4: Identify any groups of three from the prime factorization.
∛(-72) = ∛(-1) × ∛(2^3) × ∛(3^2)
Step 5: Simplify the cube roots of the individual numbers.
∛(-72) = -1 × 2 × 3 = -6
Therefore, the simplified cube root of -72 is -6.
To simplify the cube root (∛) of -72, we need to find the number that, when cubed, results in -72. The cube root asks "what number, when multiplied by itself twice, equals -72?"
To find the cube root, we can use the fact that -72 is negative. When we simplify a cube root of a negative number, the answer will also be negative because multiplying two negative numbers gives a positive result.
To find the numerical value of the simplified cube root, we start by finding the prime factors of 72:
72 = 2 × 2 × 2 × 3 × 3
Next, we group the prime factors in groups of three because we are looking for the cube root:
72 = (2 × 2 × 2) × (3 × 3)
Now we can simplify the cube root:
∛-72 = ∛[(2 × 2 × 2) × (3 × 3)] = ∛[(2³) × (3²)]
Since ∛(2³) = 2 and ∛(3²) = 3, we can simplify further:
∛-72 = 2 × 3 = 6
Therefore, the simplified cube root (∛) of -72 is -6.