What is ³√54 simplified.
The cube root of 54 simplified is ³√54 = ³√(27 * 2) = ³√27 * ³√2 = 3 * √2 = 3√2.
To simplify the cube root of 54, you can break down 54 into its prime factors.
Start by dividing 54 by the smallest prime number, which is 2.
54 ÷ 2 = 27
Next, divide 27 by another prime number, 3.
27 ÷ 3 = 9
Finally, divide 9 by 3 again.
9 ÷ 3 = 3
Since there are no more prime factors left, you can see that the prime factorization of 54 is 2 x 3 x 3 x 3.
Now, you can pair up the factors in groups of three.
∛(2 x 3 x 3 x 3) = ∛(2 x 3²)
Finally, simplify each pair.
∛(2 x 3²) = ∛(2) x ∛(3²) = ∛2 x 3
Therefore, the simplified cube root of 54 is ∛2 x 3.
To simplify the cube root of 54, we need to find the largest perfect cube that is a factor of 54. Here's how you can find the solution:
1. Begin by listing the prime factors of 54: 54 = 2 * 3 * 3 * 3.
2. Group the factors in sets of three to look for perfect cubes: 54 = 2 * (3 * 3 * 3).
3. Simplify the grouped factors: 54 = 2 * (3^3).
4. Rewrite the expression without the perfect cube: 54 = 2 * ³√(3^3).
5. Finally, simplify this expression: 54 = 2 * ³√27 = 2 * 3 = 6.
So, the simplified cube root of 54 is 6.