What is ∛54 simplified?:?
The cube root of 54 simplified is 3√6.
To simplify ∛54, we need to find the prime factors of 54 and group them in triples.
The prime factors of 54 are 2, 3, and 3.
Grouping these factors in triples, we have (2)(3)(3).
Multiplying these factors, we get the simplified cube root:
∛54 = 2∛3
To simplify the cube root of 54 (∛54), you need to find the perfect cube(s) that divides 54. Here's how you can do it step by step:
1. Begin by factoring 54 into its prime factors: 54 = 2 × 3 × 3 × 3.
2. Group the factors into triples of three. In this case, we have a triple of 3s.
3. Take one factor from each group, in this case, one 3.
4. Write down the remaining factors not used in triples, which are 2 × 3.
5. Simplify the cube root by writing the result as the product of the factor(s) outside the cube root and the factor(s) inside it.
In this case, ∛54 simplifies to ∛(2 × 3 × 3 × 3) = 3∛2.
Therefore, the simplified form of ∛54 is 3∛2.