What is ∛54 simplified????
The simplified cube root of 54 is approximately 3.78.
To simplify the cube root of 54 (∛54), you need to find the prime factors of 54 and simplify them.
First, you can start by dividing 54 by 2, since it is an even number. 54 divided by 2 is 27.
Next, we can continue dividing by 3, since 27 is divisible by 3. 27 divided by 3 is 9.
Finally, we can divide 9 by 3 again. 9 divided by 3 is 3.
So, the prime factorization of 54 is 2 × 3 × 3 × 3.
Now, we can simplify the cube root of 54:
∛(54) = ∛(2 × 3 × 3 × 3)
Taking one factor of 3 outside the cube root:
= 3 × ∛(2 × 3 × 3)
= 3 × ∛(18)
Therefore, the simplified form of ∛54 is 3∛18.
To simplify the cubic root (∛) of 54, we need to find the largest perfect cube that is a factor of 54. Here's how you can do it step by step:
1. Start by listing the prime factors of 54: 54 = 2 × 3 × 3 × 3.
2. Look for groups of three identical prime factors. Here, we have three 3's, which can be written as 3^3.
3. Rewrite the expression using the largest perfect cube factor: ∛54 = ∛(2 × 3^3).
4. Simplify the expression: ∛(2 × 3^3) = ∛(2 × 27).
5. Calculate the cubic root of 27: ∛27 = 3.
6. Combine all the simplified terms: ∛(2 × 27) = 3∛2.
7. So, the simplified form of ∛54 is 3∛2.