Evaluate fourth root of 1296

Problem

√(4,1296)

Solution

1. Identify the number to be evaluated, which is 1296 and the root to be taken, which is the fourth root.

2. Prime factorize the number 1296 to see if it can be expressed as a power of an integer.

3. Divide 1296 by 2 repeatedly:

1296=2×648

648=2×324

324=2×162

162=2×81

4. Factor the remaining number 81 using 3

81=3×27

27=3×9

9=3×3

5. Group the prime factors to write the number in exponential form:

1296=2×3

6. Apply the property of exponents (a×b)n=an×bn

1296=(2×3)4

1296=6

7. Evaluate the fourth root by taking the base of the power:

√(4,6)=6

Final Answer

√(4,1296)=6

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