Simplify cube root of 729

Problem

√(3,729)

Solution

1. Identify the number under the radical, which is 729

2. Determine the prime factorization of 729 by dividing by 3 repeatedly.

3. Calculate the factors: 729=3×243=3^2×81=3^3×27=3^4×9=3^5×3=3^6

4. Rewrite the expression using the exponent form of the cube root, which is a^1/3

5. Apply the power of a power rule: (3^6)^1/3=3^(6×1/3)=3^2

6. Evaluate the resulting power: 3^2=9

Final Answer

√(3,729)=9

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