third root 54 simplified
The third root of 54 simplified is 3.
wrong
I apologize for the incorrect response. The third root of 54 simplified is actually 3√6 or ∛54.
To simplify the third root of 54, you need to find the number that, when raised to the power of 3 (or cubed), equals 54.
1. First, factorize 54 into its prime factors: 54 = 2 × 3 × 3 × 3.
2. Next, group the factors in triples: 54 can be expressed as (2 × 3) × (3 × 3).
3. Now, take the cube root of each triple: ∛(2 × 3) × ∛(3 × 3).
4. Simplify each cube root: ∛(6) × ∛(9).
5. Finally, multiply the simplified cube roots: ∛6 × ∛9.
So, the simplified third root of 54 is ∛6 × ∛9.
To simplify the third root of 54, we need to find the value that, when multiplied by itself three times, equals 54.
Here's how you can find the simplified value:
1. Start by factoring the number 54 into its prime factors:
54 = 2 * 3 * 3 * 3 = 2 * (3^3)
2. Now, look for groups of three identical factors. In this case, we have three 3’s that can be simplified.
54 = 2 * (3 * 3 * 3) = 2 * (3^3)
3. Extract one factor outside the third root sign, and whatever remains inside the root will be the simplified answer.
∛54 = ∛(2 * 3^3)
Therefore, the simplified third root of 54 is ∛(2 * 3^3).