Simplify ^3√54
^3√54 can be simplified as follows:
Step 1: Find the prime factorization of 54:
54 = 2 * 3 * 3 * 3 = 2 * 3^3
Step 2: Extract the cube root from each factor:
^3√54 = ^3√(2 * 3^3)
Step 3: Simplify the cube root:
^3√2 * ^3√3^3 = ^3√2 * 3 = 3√2
Therefore, ^3√54 simplifies to 3√2.
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The cube root of 54 can be simplified as follows:
Step 1: Find the prime factorization of 54:
54 = 2 * 3 * 3 * 3 = 2 * 3^3
Step 2: Simplify the cube root:
∛54 = ∛(2 * 3^3)
Step 3: Take out the cube root of each factor:
∛2 * ∛(3^3) = ∛2 * 3
Therefore, ∛54 simplifies to 3∛2.
To simplify the cube root of 54, you can follow these steps:
1. Prime factorize 54: Start by finding the prime factors of 54, which are 2, 3, and 3. So, 54 can be written as 2 * 3 * 3.
2. Rewrite the expression: Express the cube root of 54 as the product of the cube root of each factor. In this case, it becomes ^3√(2 * 3 * 3).
3. Simplify the expression: Since there are three factors of 3, you can take one factor out of the cube root. So, ^3√(2 * 3 * 3) simplifies to 3 * ^3√2.
Therefore, the simplified form of ^3√54 is 3 * ^3√2.
To simplify ^3√54, prime factorize 54 and rewrite it using exponents.
54 = 2 × 3 × 3 × 3
Now, group the prime factors into sets of three, since we are taking the cube root.
^3√(2 × 3 × 3 × 3)
= ^3√(2 × 3^3)
= 2 × ^3√3^3
= 2 × 3
= 6
Therefore, ^3√54 simplified is equal to 6.