Evaluate fifth root of 96

Problem

√(5,96)

Solution

1. Identify the expression as the fifth root of the integer 96.

2. Find the prime factorization of 96 by dividing by the smallest prime numbers.

96=2×48

48=2×24

24=2×12

12=2×6

6=2×3

3. Rewrite the number 96 using its prime factors to identify any perfect fifth powers.

96=2×3

4. Apply the property of radicals √(n,a×b)=√(n,a)×√(n,b) to separate the factors.

√(5,96)=√(5,2×3)

√(5,96)=√(5,2)×√(5,3)

5. Simplify the radical by evaluating the fifth root of the perfect fifth power.

√(5,2)=2

√(5,96)=2√(5,3)

Final Answer

√(5,96)=2√(5,3)

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