Evaluate square root of 729

Problem

√(,729)

Solution

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

2. Determine the prime factorization of the number to see if it is a perfect square.

729=3⋅243

729=3⋅3⋅81

729=3⋅3⋅3⋅3⋅3⋅3

729=3

3. Apply the property of square roots √(,xn)=x(n/2) to evaluate the expression.

√(,3)=3(6/2)

3=27

4. Verify the result by squaring the value.

27⋅27=729

Final Answer

√(,729)=27

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