Simplify fifth root of 96+ fifth root of 3

Problem

√(5,96)+√(5,3)

Solution

1. Factor the radicand of the first term to identify perfect fifth powers.

96=32⋅3

2. Rewrite the first term using the prime factorization, noting that 32=2

√(5,2⋅3)+√(5,3)

3. Apply the product property of radicals, √(n,a*b)=√(n,a)⋅√(n,b) to simplify the first term.

2√(5,3)+√(5,3)

4. Combine like terms by adding the coefficients of the identical radical parts.

(2+1)√(5,3)

5. Simplify the resulting expression.

3√(5,3)

Final Answer

√(5,96)+√(5,3)=3√(5,3)

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