Evaluate cube root of 729

Problem

√(3,729)

Solution

1. Identify the number whose cube root needs to be found, which is 729

2. Prime factorize the number to see if it is a perfect cube.

729=3×243

729=3×3×81

729=3×3×3×27

729=3×3×3×3×3×3

3. Group the prime factors into sets of three.

729=(3×3×3)×(3×3×3)

729=3×3

4. Apply the property of exponents (a×b)n=an×bn to rewrite the expression.

729=(3×3)3

729=9

5. Evaluate the cube root by taking the base of the cubed value.

√(3,729)=9

Final Answer

√(3,729)=9

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