What is ^3√54 simplified?
^3√54 simplified is 3√2.
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To simplify the cube root of 54 (∛54), we can factorize 54 as the product of its prime factors:
54 = 2 * 3 * 3 * 3 = 2 * 3^3
Taking the cube root of each factor, we get:
∛54 = ∛(2 * 3^3) = ∛2 * ∛3^3 = ∛2 * 3
Thus, ∛54 simplified is 3∛2.
To simplify the cube root of 54, also represented as ^3√54, follow these steps:
Step 1: Find the prime factors of 54. Prime factors are the prime numbers that, when multiplied together, give the original number.
Prime factorization of 54:
54 = 2 × 27
54 = 2 × 3 × 9
54 = 2 × 3 × 3 × 3
Step 2: Group the prime factors in sets of three, as we are dealing with a cube root.
^3√54 = ^3√(2 × 3 × 3 × 3)
^3√54 = ^3√(2 × 3^3)
Step 3: Remove one factor from each group and bring it outside the cube root.
^3√54 = 3√(2)
Therefore, the simplified form of ^3√54 is 3√2.
To simplify ^3√54, you need to find the cube root of 54. Here's how you can do it:
1. Prime factorize 54: 54 = 2 * 3^3
2. Rewrite 54 using its prime factorization: ^3√(2 * 3^3)
3. Separate the cube root of the prime factors: ^3√2 * ^3√(3^3)
4. Simplify each cube root: ^3√2 * 3
So, ^3√54 simplified is 3√2.