What is ³√54 simplified
³√54 simplified is 3√2+√6
To simplify the cube root of 54, you need to find the largest perfect cube that divides 54. Let's find it step by step:
1. Prime factorize 54:
54 = 2 * 3 * 3 * 3
2. Group the prime factors in triples:
54 = (2 * 3 * 3) * 3
3. Take out a triplet from under the cube root:
³√54 = ³√(2 * 3 * 3) * ³√3
4. Simplify the triplet under the cube root:
³√(2 * 3 * 3) = 3 * ³√2
5. Simplify the remaining number under the cube root:
³√3 = 3√3
So, the simplified form of the cube root of 54 is:
³√54 = 3 * ³√2 * 3√3
To simplify the cube root of 54, we need to find a whole number that, when multiplied by itself three times, equals 54.
Here is one way to approach this problem:
1. Prime factorize 54: 54 = 2 * 3 * 3 * 3.
2. Group the factors into triples: 54 = 2 * (3 * 3 * 3).
3. Look for three identical factors within the parentheses. In this case, we have three 3's.
4. Pull out one 3 from the parentheses and leave the other two inside: 54 = 2 * 3 * (3 * 3).
5. Simplify the remaining expression inside the parentheses: 54 = 2 * 3 * 9.
6. Multiply the factors outside the parentheses: 54 = 6 * 9.
7. Simplify further: 54 = 54.
Therefore, the simplified form of the cube root of 54 is ³√54 = ³√(2 * 3 * 3 * 3) = ³√(2 * 3 * 9) = ³√(6 * 9) = 6.