What is ^3√54 simplified?
The simplified form of ^3√54 is 3√2.
To simplify ^3√54, we need to find the cube root of 54.
First, we can find the prime factorization of 54.
54 = 2 × 3 × 3 × 3
Now, we can group the prime factors in sets of three:
(2 × 3 × 3) × 3
Since we are taking the cube root, we can pull out one factor from each group:
2 × 3 × ^3√3
Therefore, the simplified form of ^3√54 is 2 × 3 × ^3√3.
To simplify the cube root of 54, we need to find the largest perfect cube that divides evenly into 54. One way to do this is by trial and error. We can start by trying to find the perfect cube root of 54.
Let's start with the cube of 2: 2^3 = 8, which is less than 54.
Next, we try 3: 3^3 = 27, which is also less than 54.
Then, we try 4: 4^3 = 64, which is greater than 54.
Since 4^3 is greater than 54 and 3^3 is less than 54, the largest perfect cube that divides evenly into 54 is 3^3, which is equal to 27.
Therefore, ^3√54 simplified is equal to 3.